A220889 a(n) = F(n+8) - (1/6)*(n^4-2*n^3+26*n^2+47*n+132) where F(i) = Fibonacci numbers (A000045).

0, 0, 0, 0, 1, 8, 35, 113, 303, 717, 1552, 3145, 6062, 11242, 20230, 35554, 61335, 104274, 175249, 291899, 482805, 794255, 1301190, 2124915, 3461756, 5629428, 9142060, 14831588, 24044173, 38958012, 63097567, 102165605, 165389467, 267699377, 433253020, 701138429, 1134601450

Offset

1,6

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

J. Freixas and S. Kurz, The golden number and Fibonacci sequences in the design of voting structures, 2012.

J. Freixas and S. Kurz, The golden number and Fibonacci sequences in the design of voting structures, arXiv:1401.8180 [math.CO], 2014.

Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1).

Formula

G.f.: x^5*(x+1)^2 / ((x-1)^5*(x^2+x-1)). [Colin Barker, Jan 03 2013]

Mathematica

Table[Fibonacci[n + 8] - n*(n*(n*(n - 2) + 26) + 47)/6 - 22, {n, 50}] (* or *)
LinearRecurrence[{6, -14, 15, -5, -4, 4, -1}, {0, 0, 0, 0, 1, 8, 35}, 50] (* Paolo Xausa, Mar 19 2024 *)

Crossrefs

Cf. A000045.

Sequence in context: A266785 A267170 A266762 * A285240 A036598 A229403

Adjacent sequences: A220886 A220887 A220888 * A220890 A220891 A220892

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 29 2012

Status

approved