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

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

Offset: 0

Author

Paul Barry, Feb 16 2004

Keywords

• easy
• nonn

Comments

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

References

• S. 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).

Crossrefs

Cf. A091927, A015553.

Programs

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 *)

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).