A015551 Expansion of x/(1 - 6*x - 5*x^2).

0, 1, 6, 41, 276, 1861, 12546, 84581, 570216, 3844201, 25916286, 174718721, 1177893756, 7940956141, 53535205626, 360916014461, 2433172114896, 16403612761681, 110587537144566, 745543286675801, 5026197405777636

Offset

0,3

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)=(B^n)_1,2 for instance. - Paul Barry, Feb 13 2004

Pisano period lengths: 1, 2, 4, 4, 1, 4, 42, 8, 12, 2, 10, 4, 12, 42, 4, 16, 96, 12, 360, 4, ... - R. J. Mathar, Aug 10 2012

Links

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

Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.

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

Formula

a(n) = 6*a(n-1) + 5*a(n-2).

a(n) = sqrt(14)*(3+sqrt(14))^n/28 - sqrt(14)*(3-sqrt(14))^n/28. - Paul Barry, Feb 13 2004

Mathematica

Join[{a=0, b=1}, Table[c=6*b+5*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
CoefficientList[Series[x/(1-6x-5x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[ {6, 5}, {0, 1}, 30] (* Harvey P. Dale, Oct 30 2017 *)

Prog

(Sage) [lucas_number1(n, 6, -5) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) I:=[0, 1]; [n le 2 select I[n] else 6*Self(n-1)+5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2011
(PARI) a(n)=([0, 1; 5, 6]^n*[0; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A015548, A030195, A053404, A057087, A057088, A057089, A083858, A085939, A090017, A091914, A099012, A135030, A135032, A180222, A180226, A180250.

Sequence in context: A323969 A252980 A274997 * A291018 A227214 A049685

Adjacent sequences: A015548 A015549 A015550 * A015552 A015553 A015554

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved