A136429 a(n) = Sum_{k=0..n} F(k+1)^2*F(n-k+1)^2 where F = Fibonacci numbers (A000045).

1, 2, 9, 26, 84, 250, 747, 2182, 6323, 18132, 51624, 146004, 410677, 1149578, 3204477, 8899502, 24634620, 67990414, 187154271, 513939214, 1408246247, 3851081256, 10512259920, 28647203880, 77946605545, 211782868754

Offset

0,2

Comments

Also: the self-convolution of A007598, after A007598(0) is dropped. - R. J. Mathar, Aug 05 2008

a(n) is the number of ways to tile a 2 X (n+1) board with squares and dominoes with exactly one vertical domino. - Greg Dresden and Zijie He, Jun 14 2022

Links

Emanuele Munarini, Apr 01 2008, Table of n, a(n) for n = 0..100

Ömer Egecioglu, Elif Saygi, and Zülfükar Saygi, The Mostar index of Fibonacci and Lucas cubes, arXiv:2101.04740 [math.CO], 2021. Mentions this sequence.

Index entries for linear recurrences with constant coefficients, signature (4,0,-10,0,4,-1).

Formula

G.f.: (1-x)^2/((1+x)^2*(1-3x+x^2)^2).

Recurrence: a(n+6) = 4a(n+5) - 10a(n+3) + 4a(n+1) - a(n).

Mathematica

LinearRecurrence[{4, 0, -10, 0, 4, -1}, {1, 2, 9, 26, 84, 250}, 30] (* Harvey P. Dale, Oct 03 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, fibonacci(k+1)^2*fibonacci(n-k+1)^2); \\ Michel Marcus, Jan 13 2021

Crossrefs

Cf. A000045, A007598.

Sequence in context: A014150 A213387 A215184 * A091469 A125670 A222660

Adjacent sequences: A136426 A136427 A136428 * A136430 A136431 A136432

Keyword

easy,nonn

Author

Emanuele Munarini, Apr 01 2008

Status

approved