A023615 Convolution of Fibonacci numbers and primes.

2, 5, 12, 24, 47, 84, 148, 251, 422, 702, 1155, 1894, 3090, 5027, 8164, 13244, 21467, 34772, 56306, 91149, 147528, 238756, 386367, 625212, 1011676, 1636989, 2648768, 4285864, 6934741, 11220718, 18155586, 29376435, 47532158, 76908732, 124441039, 201349922

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..4775

Formula

a(n) = Sum_{1<=k<=n+1} A000040(k)*A000045(n+2-k). - Robert Israel, Jan 18 2018

a(n) = a(n-1) + a(n-2) + prime(n+1). - Alois P. Heinz, Feb 19 2023

Maple

N:= 100: # to get a(0)..a(N)
G:= add(ithprime(i)*x^(i-1), i=1..N+1):
S:= series(G /(1-x-x^2), x, N+1):
seq(coeff(S, x, n), n=0..N); # Robert Israel, Jan 18 2018
# second Maple program:
a:= proc(n) option remember; `if`(n<0, 0,
      a(n-1)+a(n-2)+ithprime(n+1))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Feb 19 2023

Crossrefs

Cf. A000040, A000045, A023608.

Sequence in context: A116713 A261369 A116714 * A320235 A034483 A267004

Adjacent sequences: A023612 A023613 A023614 * A023616 A023617 A023618

Keyword

nonn

Author

Clark Kimberling

Status

approved