A067430 Convolution of Fibonacci F(n+1), n>=0, with F(n+7), n>=0.

13, 34, 81, 170, 340, 654, 1227, 2258, 4095, 7340, 13032, 22956, 40169, 69890, 121005, 208606, 358268, 613242, 1046535, 1781170, 3024123, 5123104, 8661456, 14616600, 24624325, 41419234, 69568137, 116690258, 195485860, 327106470, 546750147, 912944786, 1522940919, 2538219860

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Formula

a(n)= A067330(n+6, n) = A067418(n+6, 6)= sum(F(k+1)*F(n+7-k), k=0..n), n>=0.

a(n)= ((47*n+65)*F(n+1)+29*(n+1)*F(n))/5, where F(n) = A000045(n) (Fibonacci).

G.f.: (13+8*x)/(1-x-x^2)^2.

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4). - Paolo Xausa, Jun 23 2026

Mathematica

A067430[n_] := ((47*n + 65)*Fibonacci[n+1] + 29*(n+1)*Fibonacci[n])/5;
Array[A067430, 35, 0] (* Paolo Xausa, Jun 23 2026 *)
(* Alternative: *)
LinearRecurrence[{2, 1, -2, -1}, {13, 34, 81, 170}, 35] (* Paolo Xausa, Jun 23 2026 *)

Crossrefs

Seventh diagonal of A067330. Seventh column of A067418.

Cf. A000045.

Sequence in context: A081752 A069484 A089113 * A214729 A280322 A262851

Adjacent sequences: A067427 A067428 A067429 * A067431 A067432 A067433

Keyword

nonn,easy,changed

Author

Wolfdieter Lang, Feb 15 2002

Extensions

More terms from Paolo Xausa, Jun 23 2026

Status

approved