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 A015551 Expansion of x/(1 - 6*x - 5*x^2). 6
 0, 1, 6, 41, 276, 1861, 12546, 84581, 570216, 3844201, 25916286, 174718721, 1177893756, 7940956141, 53535205626, 360916014461, 2433172114896, 16403612761681, 110587537144566, 745543286675801, 5026197405777636 (list; graph; refs; listen; history; text; internal format)
 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 STATUS approved

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Last modified December 3 20:52 EST 2022. Contains 358543 sequences. (Running on oeis4.)