Lucas Numbers – A term is sum of immediate previous two terms. Starting two terms are 2 & 1. So, these are like Fibonacci numbers but starting two terms in Fibonacci numbers are 0 & 1. List the product of first 20 Fibonacci & Lucas numbers term by term. Hence F1*L1, F2*L2, F3*L3….F20*L20 need to be listed. For reference purpose to know how the answer was arrived (in your solution, you will need to generate these) – First 20 Fibonacci numbers = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181 First 20 Lucas numbers = 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349 Unconfirmed Fact – It was Edouard Lucas who coined the term Fibonacci numbers.
📌 Challenge Details and Links
ExcelBI Excel Challenge Number: 376
Challenge Difficulty: ⭐️
📥Download Sample File
📥Link to the solutions on LinkedIn
Solving the challenge of Multiply Fibonacci and Lucas Numbers with Power Query
Power Query solution 1 for Multiply Fibonacci and Lucas Numbers, proposed by John V.:
let
b = {0..19}, f = (i) => List.Accumulate(b, {i, 1}, (s, c) => s & {List.Sum(List.LastN(s, 2))})
in
List.Transform(b, each f(0){_} * f(2){_})
or ( محمد حلمي
idea : )
✅
= List.Accumulate({0..18}, {0}, (s, c) => s & {1 + List.Sum(s) + List.Max(s)})
Blessings!
Power Query solution 2 for Multiply Fibonacci and Lucas Numbers, proposed by Alejandro Simón 🇵🇦 🇪🇸:
let
Fib = List.Generate(
() => [x = 1, y = 0, z = 0],
each [z] < 20,
each [x = [y], y = [x] + [y], z = [z] + 1],
each [y]
),
Lucas = List.Generate(
() => [x = 2, y = 1, z = 0],
each [z] < 20,
each [x = [y], y = [x] + [y], z = [z] + 1],
each [x]
),
Sol = List.Transform({0 .. List.Count(Fib) - 1}, each Fib{_} * Lucas{_})
in
SolPower Query solution 3 for Multiply Fibonacci and Lucas Numbers, proposed by An Nguyen:
let
GenerateFibo = List.Accumulate(
List.Buffer({1 .. 38}),
[r = {0, 1}],
(state, current) =>
[Currentvalue = List.Sum(List.LastN(state[r], 2)), r = state[r] & {Currentvalue}]
)[r],
MakeTable = Table.FromColumns({GenerateFibo}, {"Fibonacci Numbers"}),
AddIdx = Table.AddIndexColumn(MakeTable, "Idx"),
Result = Table.SelectRows(AddIdx, each Number.IsEven([Idx]))[Fibonacci Numbers]
in
ResultPower Query solution 4 for Multiply Fibonacci and Lucas Numbers, proposed by Ramiro Ayala Chávez:
let
a = List.Generate(
() => [x = 0, y = 1, c = 1],
each [c] <= 20,
each [y = [x] + [y], x = [y], c = [c] + 1],
each [x]
),
b = List.Generate(
() => [x = 2, y = 1, c = 1],
each [c] <= 20,
each [y = [x] + [y], x = [y], c = [c] + 1],
each [x]
),
c = List.Transform({0 .. 19}, each a{_} * b{_}),
Sol = Table.FromColumns({c}, {"Answer Expected"})
in
SolPower Query solution 5 for Multiply Fibonacci and Lucas Numbers, proposed by Rafael González B.:
Hi Everyone, my {M} code:
FibLuc =
List.Generate(
() => [i = 1, X = 0, Y = 1, X1 = 2, Y1 = 1],
each [i] <= 20,
each [
i = [i] + 1,
X = [Y],
Y = [X] + [Y],
X1 = [Y1],
Y1 = [X1] + [Y1]
],
each [X] * [X1]
)
in
FibLuc
Power Query solution 6 for Multiply Fibonacci and Lucas Numbers, proposed by Arden Nguyen, CPA:
let
n = 20,
fn = (i as number, x1 as number, x2 as number, optional L as list) =>
let
a = L ?? {x1} & {x2},
b =
if i <= n - 2 then
@fn(i + 1, x1, x2, a & {List.Sum(List.LastN(a, 2))})
else if n > 1 then
a
else
{x1}
in
b,
res = List.Transform(List.Zip({fn(1, 0, 1), fn(1, 2, 1)}), List.Product)
in
resSolving the challenge of Multiply Fibonacci and Lucas Numbers with Excel
Excel solution 1 for Multiply Fibonacci and Lucas Numbers, proposed by Bo Rydobon 🇹🇭:
=TAKE(
WRAPROWS(
REDUCE(
{0;1},
SEQUENCE(
38
),
LAMBDA(
a,
v,
VSTACK(
a,
SUM(
TAKE(
a,
-2
)
)
)
)
),
2
),
,
1
)Excel solution 2 for Multiply Fibonacci and Lucas Numbers, proposed by Rick Rothstein:
=LET(
f,
LAMBDA(
x,
y,
REDUCE(
VSTACK(
x,
y
),
SEQUENCE(
18
),
LAMBDA(
a,
v,
VSTACK(
a,
SUM(
TAKE(
a,
-2
)
)
)
)
)
),
f(
0,
1
)*f(
2,
1
)
)Excel solution 3 for Multiply Fibonacci and Lucas Numbers, proposed by John V.:
=LET(
f,
LAMBDA(
i,
REDUCE(
i,
ROW(
1:18
),
LAMBDA(
a,
v,
VSTACK(
a,
SUM(
TAKE(
a,
-2
)
)
)
)
)
),
f(
{0;1}
)*f(
{2;1}
)
)Excel solution 4 for Multiply Fibonacci and Lucas Numbers, proposed by محمد حلمي:
=INDEX(
REDUCE(
{0;1},
SEQUENCE(
38
),
LAMBDA(
a,
d,
VSTACK(
a,
SUM(
TAKE(
a,
-2
)
)
)
)
),
SEQUENCE(
20,
,
,
2
)
)Excel solution 5 for Multiply Fibonacci and Lucas Numbers, proposed by محمد حلمي:
=REDUCE(
{0;1},
SEQUENCE(
18
),
LAMBDA(
a,
d,
VSTACK(
a,
SUM(
a,
MAX(
a
),
1
)
)
)
)Excel solution 6 for Multiply Fibonacci and Lucas Numbers, proposed by محمد حلمي:
=REDUCE(
{0;1},
SEQUENCE(
18
),
LAMBDA(
a,
d,
VSTACK(
a,
SUM(
a
)+TAKE(
a,
-1
)+1
)
)
)Excel solution 7 for Multiply Fibonacci and Lucas Numbers, proposed by Kris Jaganah:
=TAKE(WRAPROWS(REDUCE({0;1},
SEQUENCE(
38
),
LAMBDA(x,
y,
VSTACK(x,
SUM((TAKE(
x,
-2
)))))),
2),
,
1)Excel solution 8 for Multiply Fibonacci and Lucas Numbers, proposed by Timothée BLIOT:
=LET(
A,
LAMBDA(
x,
y,
REDUCE(
VSTACK(
x,
y
),
SEQUENCE(
18
),
LAMBDA(
a,
v,
VSTACK(
a,
SUM(
TAKE(
a,
-2
)
)
)
)
)
),
A(
0,
1
)*A(
2,
1
)
)Excel solution 9 for Multiply Fibonacci and Lucas Numbers, proposed by Sunny Baggu:
=LET(
_e1,
LAMBDA(
arr,
REDUCE(
arr,
SEQUENCE(
20
),
LAMBDA(
A,
V,
VSTACK(
A,
SUM(
TAKE(
A,
-2
)
)
)
)
)
),
TAKE(_e1({0; 1}) * _e1({2; 1}),
20)
)Excel solution 10 for Multiply Fibonacci and Lucas Numbers, proposed by LEONARD OCHEA 🇷🇴:
=LET(s,
2*(ROW(
1:20
)-1),
x,
5^0.5,
y,
(1+x)/2,
z,
y-x,
(y^s-z^s)/x)Excel solution 11 for Multiply Fibonacci and Lucas Numbers, proposed by Abdallah Ally:
=LET(
n,
20,
f,
LAMBDA(
f,
a,
b,
IF(
b=n,
a,
f(
f,
VSTACK(
a,
SUM(
TAKE(
a,
-2
)
)
),
b+1
)
)
),
f(
f,
{0;1},
2
)*f(
f,
{2;1},
2
)
)Excel solution 12 for Multiply Fibonacci and Lucas Numbers, proposed by An Nguyen:
=LET(p,
(1+SQRT(
5
))/2,
f,
LAMBDA(x,
(p^x-(1-p)^x)/SQRT(
5
)),
f(
SEQUENCE(
20,
,
0
)
)*VSTACK(
2,
1,
ROUND(
p^SEQUENCE(
18,
,
2
),
0
)
))Excel solution 13 for Multiply Fibonacci and Lucas Numbers, proposed by Charles Roldan:
=LET(f,
LAMBDA(
G,
G(
G
)
)(LAMBDA(g,
LAMBDA(a,
n,
IF(n <= COUNTA(
a
),
TAKE(
a,
n
),
LAMBDA(
x,
VSTACK(
x,
SUM(
TAKE(
x,
-2
)
)
)
)(g(
g
)(a,
n - 1)))))),
f(
{0; 1},
20
) * f(
{2; 1},
20
))Excel solution 14 for Multiply Fibonacci and Lucas Numbers, proposed by Charles Roldan:
=INT(((1+SQRT(
5
))/2)^(2*SEQUENCE(
20,
,
0
))/SQRT(
5
))Excel solution 15 for Multiply Fibonacci and Lucas Numbers, proposed by Bilal Mahmoud kh.:
=REDUCE(
0,
ROW(
1:20
),
LAMBDA(
x,
y,
VSTACK(
x,
IFERROR(
LARGE(
x,
1
)+LARGE(
x,
2
),
1
)
)
)
)
and for the Lucas series,
we can generate by the following formula:
=REDUCE(
2,
ROW(
1:20
),
LAMBDA(
x,
y,
IF(
LARGE(
x,
1
)<>3,
VSTACK(
x,
IFERROR(
LARGE(
x,
1
)+LARGE(
x,
2
),
1
)
),
VSTACK(
x,
IFERROR(
LARGE(
x,
1
)+SMALL(
x,
1
),
1
)
)
)
)
)Excel solution 16 for Multiply Fibonacci and Lucas Numbers, proposed by JvdV -:
=REDUCE(
,
ROW(
1:20
)-1,
LAMBDA(
x,
y,
VSTACK(
x,
SUM(
x,
MAX(
x
),
1
)
)
)
)Excel solution 17 for Multiply Fibonacci and Lucas Numbers, proposed by Pieter de Bruijn:
=REDUCE(
,
SEQUENCE(
20
)-1,
LAMBDA(
x,
y,
VSTACK(
x,
SUM(
x,
MAX(
x
),
1
)
)
)
)Excel solution 18 for Multiply Fibonacci and Lucas Numbers, proposed by Pieter de Bruijn:
=LET(
z,
LAMBDA(
x,
y,
REDUCE(
VSTACK(
x,
y
),
ROW(
1:18
),
LAMBDA(
x,
y,
VSTACK(
x,
SUM(
TAKE(
x,
-2
)
)
)
)
)
),
z(
0,
1
)*z(
2,
1
)
)Excel solution 19 for Multiply Fibonacci and Lucas Numbers, proposed by Giorgi Goderdzishvili:
=LET(
lst,
SCAN(
"0!1",
SEQUENCE(
75
),
LAMBDA(
a,
v,
CONCAT(
TAKE(
TEXTSPLIT(
a,
"!"
),
& ,
-1
),
"!",
SUM(
--TEXTSPLIT(
a,
"!"
)
)
)
)
),
tx,
VSTACK(
0,
1*TEXTBEFORE(
lst,
"!"
)
),
FILTER(
TAKE(
tx,
40
),
ISODD(
--SEQUENCE(
40
)
)
)
)Excel solution 20 for Multiply Fibonacci and Lucas Numbers, proposed by Arden Nguyen, CPA:
=LET(
a,
LAMBDA(
x,
REDUCE(
VSTACK(
x,
1
),
SEQUENCE(
18,
,
2
),
LAMBDA(
s,
c,
VSTACK(
s,
INDEX(
s,
c
) + INDEX(
s,
c - 1
)
)
)
)
),
a(
2
)*a(
0
)
)Solving the challenge of Multiply Fibonacci and Lucas Numbers with Python
Python solution 1 for Multiply Fibonacci and Lucas Numbers, proposed by John V.:
Hi everyone!
def s(i, n):
p = [i, 1]
[p.append(p[-2] + p[-1]) for _ in range(2, 1+n)]
return p
[a * b for a, b in zip(s(0, 19), s(2, 19))]
s = [0]
[s.append(1 + sum(s) + s[-1]) for _ in range(1, 20)]
s
Blessings!
Python solution 2 for Multiply Fibonacci and Lucas Numbers, proposed by Giorgi Goderdzishvili:
srt_lst = [0,1]
for k in range(0,20):
for i in range(50):
new = srt_lst[-2] + srt_lst[-1]
srt_lst.append(new)
print(srt_lst[2*k])
Python solution 3 for Multiply Fibonacci and Lucas Numbers, proposed by Jan Willem Van Holst:
in Python:
import numpy as np
fib = [0,1]
luc = [2,1]
for i in range(2,20):
new = fib[i-2]+fib[i-1]
fib.append(new)
new = luc[i-2]+luc[i-1]
luc.append(new)
answer = np.array(fib) * np.array(luc)
Solving the challenge of Multiply Fibonacci and Lucas Numbers with R
R solution 1 for Multiply Fibonacci and Lucas Numbers, proposed by Konrad Gryczan, PhD:
library(tidyverse)
library(readxl)
test = read_excel("Excel/376 Mult of Lucas and Fibonacci.xlsx", range = "A1:A21") %>%
pull(`Answer Expected`)
if (n == 1)
return(first)
if (n == 2)
return(c(first, second))
sequence = reduce(rep(1, n - 2), function(x, y) {
c(x, sum(tail(x, 2)))
}, .init = c(first, second))
return(sequence)
}
fib = generate_sequence(20, 0, 1)
lucas = generate_sequence(20, 2, 1)
result = tibble(fib = fib,
lucas = lucas,
ratio = lucas * fib) %>%
pull(ratio)
&&