A091929 Expansion of (1-6*x)/(1-6*x-11*x^2).

1, 0, 11, 66, 517, 3828, 28655, 214038, 1599433, 11951016, 89299859, 667260330, 4985860429, 37255026204, 278374621943, 2080053019902, 15542438960785, 116135216983632, 867778130470427, 6484156169642514, 48450496453029781, 362028696584246340, 2705127640488805631

Offset

0,3

Comments

Let the generating matrix of the Golay G_24 code be [I|A]. Then a(n) = (A^n)_1,1.

References

Steven Roman, Introduction to Coding and Information Theory, Springer-Verlag, 1996, p. 224.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,11).

Formula

a(n) = (1/2 - 3*sqrt(5)/20)*(3 + 2*sqrt(5))^n + (3 - 2*sqrt(5))^n*(1/2 + 3*sqrt(5)/20).

E.g.f.: exp(3*x) * (cosh(2*sqrt(5)*x) - (3/(2*sqrt(5)))*sinh(2*sqrt(5)*x)). - Amiram Eldar, Feb 20 2026

Mathematica

CoefficientList[Series[(1-6x)/(1-6x-11x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, 11}, {1, 0}, 30] (* Harvey P. Dale, Apr 25 2018 *)

Crossrefs

Cf. A091927, A015553.

Sequence in context: A210392 A316110 A030115 * A345036 A382998 A244304

Adjacent sequences: A091926 A091927 A091928 * A091930 A091931 A091932

Keyword

easy,nonn

Author

Paul Barry, Feb 16 2004

Status

approved