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Expansion of x/(1 - 6*x - 5*x^2).
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%I #39 Sep 08 2022 08:44:40

%S 0,1,6,41,276,1861,12546,84581,570216,3844201,25916286,174718721,

%T 1177893756,7940956141,53535205626,360916014461,2433172114896,

%U 16403612761681,110587537144566,745543286675801,5026197405777636

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

%C 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

%C 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

%H Vincenzo Librandi, <a href="/A015551/b015551.txt">Table of n, a(n) for n = 0..1000</a>

%H Lucyna Trojnar-Spelina, Iwona Włoch, <a href="https://doi.org/10.1007/s40995-019-00757-7">On Generalized Pell and Pell-Lucas Numbers</a>, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,5).

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

%F a(n) = sqrt(14)*(3+sqrt(14))^n/28 - sqrt(14)*(3-sqrt(14))^n/28. - _Paul Barry_, Feb 13 2004

%t Join[{a=0,b=1},Table[c=6*b+5*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)

%t CoefficientList[Series[x/(1-6x-5x^2),{x,0,20}],x] (* or *) LinearRecurrence[ {6,5},{0,1},30] (* _Harvey P. Dale_, Oct 30 2017 *)

%o (Sage) [lucas_number1(n,6,-5) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009

%o (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

%o (PARI) a(n)=([0,1; 5,6]^n*[0;1])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016

%Y 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.

%K nonn,easy

%O 0,3

%A _Olivier Gérard_