A091927 Expansion of (1-6*x)/(1-6*x-5*x^2).

1, 0, 5, 30, 205, 1380, 9305, 62730, 422905, 2851080, 19221005, 129581430, 873593605, 5889468780, 39704780705, 267676028130, 1804580072305, 12165860574480, 82018063808405, 552937685722830, 3727716433379005, 25130987028888180, 169424504340224105, 1142201961185785530

Offset

0,3

Comments

Let the generating matrix of the Golay G_12 code be [I|B]. Then a(n) = (B^n)_1,1.

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (6,5).

Formula

a(n) = 5*(sqrt(14)*(3+sqrt(14))^(n-1)/28 - sqrt(14)*(3-sqrt(14))^(n-1)/28).

E.g.f.: exp(3*x) * (cosh(sqrt(14)*x) - (3/sqrt(14))*sinh(sqrt(14)*x)). - Amiram Eldar, Feb 20 2026

Mathematica

CoefficientList[Series[(1-6x)/(1-6x-5x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, 5}, {1, 0}, 30] (* Harvey P. Dale, Aug 11 2019 *)

Crossrefs

Cf. A015551.

Sequence in context: A245376 A118346 A234422 * A253076 A165312 A367725

Adjacent sequences: A091924 A091925 A091926 * A091928 A091929 A091930

Keyword

easy,nonn

Author

Paul Barry, Feb 13 2004

Status

approved