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A023657
Convolution of (F(2), F(3), F(4), ...) and primes.
1
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
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
KEYWORD
nonn
STATUS
approved