login
A023613
Convolution of Fibonacci numbers and A023533.
5
1, 1, 2, 4, 6, 10, 16, 26, 42, 69, 111, 180, 291, 471, 762, 1233, 1995, 3228, 5223, 8452, 13675, 22127, 35802, 57929, 93731, 151660, 245391, 397051, 642442, 1039493, 1681935, 2721428, 4403363, 7124791
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=1..n+1} A000045(k)*A023533(n+2-k). - Danny Rorabaugh, Mar 13 2015
MATHEMATICA
Join[{1, 1}, Table[Sum[Fibonacci[m+2 -Binomial[j+3, 3]], {j, 0, n}], {n, 6}, {m, Binomial[n+3, 3] -2, Binomial[n+4, 3] -3}]]//Flatten (* G. C. Greubel, Jul 14 2022 *)
PROG
(Sage) #Assuming A023533 is available as an array
for n in range(34):
print(n, sum([A023533[k]*fibonacci(n+2-k) for k in range(1, n+2)]))
# Danny Rorabaugh, Mar 14 2015
(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[Fibonacci(k)*A023533(n+2-k): k in [1..n+1]]): n in [0..50]]; // G. C. Greubel, Jul 14 2022
CROSSREFS
Sequence in context: A336662 A364580 A128588 * A306293 A307795 A065795
KEYWORD
nonn
STATUS
approved