A023557 Convolution of A023531 and Fibonacci numbers.

0, 1, 1, 2, 4, 6, 10, 16, 27, 43, 70, 113, 183, 297, 480, 777, 1257, 2034, 3291, 5326, 8617, 13943, 22560, 36503, 59063, 95566, 154630, 250196, 404826, 655022, 1059848, 1714870, 2774718, 4489588, 7264307, 11753895, 19018202, 30772097, 49790299, 80562396, 130352695, 210915091, 341267786

Offset

1,4

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = a(n-1)+a(n-2)+1 if n mod 4 = 0, else a(n) = a(n-1)+a(n-2), with offset 0. [Gary Detlefs, Dec 05 2010]

Prog

(PARI) a(n) = sum(k=1, n, issquare(8*k+9)*fibonacci(n-k+1)); \\ Michel Marcus, Jan 26 2023

Crossrefs

Cf. A000045, A023531.

Sequence in context: A293077 A000801 A080105 * A293671 A173434 A255126

Adjacent sequences: A023554 A023555 A023556 * A023558 A023559 A023560

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Michel Marcus, Jan 26 2023

Status

approved