A023657 Convolution of (F(2), F(3), F(4), ...) and primes.

2, 7, 17, 36, 71, 131, 232, 399, 673, 1124, 1857, 3049, 4984, 8117, 13191, 21408, 34711, 56239, 91078, 147455, 238677, 386284, 625123, 1011579, 1636888, 2648665, 4285757, 6934632, 11220605, 18155459, 29376304, 47532021, 76908593, 124440890, 201349771

Offset

1,1

Links

Indranil Ghosh, Table of n, a(n) for n = 1..1000

Formula

G.f.: (1/(1-x-x^2)-1)*b(x)/x, where b(x) is the g.f. of A000040. - Mario C. Enriquez, Mar 22 2017

Maple

a:= n-> add(ithprime(i)*combinat[fibonacci](n+2-i), i=1..n):
seq(a(n), n=1..40);  # Alois P. Heinz, Mar 22 2017

Mathematica

Table[Sum[Fibonacci[k + 1] Prime[n - k + 1], {k, n}], {n, 100}] (* Indranil Ghosh, Mar 22 2017 *)

Prog

(PARI) a(n) = sum(k=1, n, fibonacci(k+1)*prime(n-k+1)); \\ Michel Marcus, Mar 22 2017
(Python)
from sympy import prime, fibonacci
print([sum([fibonacci(k + 1) * prime(n - k + 1) for k in range(1, n + 1)]) for n in range(1, 101)]) # Indranil Ghosh, Mar 22 2017

Crossrefs

Sequence in context: A033937 A116576 A086717 * A045380 A086321 A009302

Adjacent sequences: A023654 A023655 A023656 * A023658 A023659 A023660

Keyword

nonn

Author

Clark Kimberling

Status

approved