A091928 a(0)=1, a(1)=5; a(n) = 6*a(n-1) + 5*a(n-2) for n > 1.

1, 5, 35, 235, 1585, 10685, 72035, 485635, 3273985, 22072085, 148802435, 1003175035, 6763062385, 45594249485, 307380808835, 2072256100435, 13970440646785, 94183924382885, 634955749531235, 4280654119101835

Offset: 0

Author

Paul Barry, Feb 13 2004

Keywords

• easy
• nonn

Comments

Let the generator matrix for the ternary Golay G_12 code be [I|B], where the elements of B are taken from the set {0,1,2}. Then a(n)=sum of first row of B^n.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,5).

Crossrefs

Cf. A015551.

Programs

Magma

[n le 2 select 5^(n-1) else 6*Self(n-1) +5*Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 27 2024

Mathematica

LinearRecurrence[{6,5},{1,5},30] (* Harvey P. Dale, Apr 09 2022 *)

SageMath

A091928= BinaryRecurrenceSequence(6,5,1,5)
[A091928(n) for n in range(41)] # G. C. Greubel, Oct 27 2024

Formula

G.f.: (1-x)/(1-6*x-5*x^2).

a(n) = (1/2 +1/sqrt(14))*(3 +sqrt(14))^n + (1/2 -1/sqrt(14))*(3 -sqrt(14))^n.

From Philippe Deléham, Sep 22 2006: (Start)

a(n) = Sum_{k=0..n} 5^k*A122542(n,k).

Lim_{n->infinity} a(n+1)/a(n) = 3 + sqrt(14) = 6.741657386773... . (End)

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007