A015553 Expansion of x/(1 - 6*x - 11*x^2).

0, 1, 6, 47, 348, 2605, 19458, 145403, 1086456, 8118169, 60660030, 453260039, 3386820564, 25306783813, 189095729082, 1412948996435, 10557746998512, 78888920951857, 589468742694774, 4404590586639071, 32911699689476940

Offset

0,3

Comments

Let the generator matrix for the binary Golay G_24 code be [I|B]. Then a(n)=(A^n)_1,2 for instance. Third binomial transform of (0,1,0,20,0,400,0,8000,...). - Paul Barry, Feb 13 2004

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 6*a(n-1) + 11*a(n-2).

a(n) = (1/4)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*4^k. - Benoit Cloitre, Oct 25 2003

a(n) = sqrt(5)(3 + 2*sqrt(5))^n/20 - sqrt(5)(3 - 2*sqrt(5))^n/20. - Paul Barry, Feb 13 2004

E.g.f.: (exp(x*(3 + 2*sqrt(5))) - exp(x*(3 - 2*sqrt(5))))/(4*sqrt(5)). - Iain Fox, Dec 31 2017

Mathematica

a[n_]:=(MatrixPower[{{1, 4}, {1, -7}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{6, 11}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)

Prog

(Sage) [lucas_number1(n, 6, -11) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 6*Self(n-1) + 11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 6*x - 11*x^2))) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A015551.

Sequence in context: A267203 A353098 A024076 * A291028 A341927 A071878

Adjacent sequences: A015550 A015551 A015552 * A015554 A015555 A015556

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved