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%I #37 Dec 18 2023 10:06:52
%S 0,1,5,32,195,1199,7360,45193,277485,1703776,10461275,64232807,
%T 394392960,2421594449,14868722965,91294775968,560554940595,
%U 3441838134751,21133075257920,129758243232857,796722742969725,4891921417478624,30036666288181195
%N Expansion of x/(1 - 5*x - 7*x^2).
%C Pisano period lengths: 1, 3, 8, 6, 8, 24, 6, 6, 24, 24, 5, 24, 12, 6, 8, 12, 16, 24, 120, 24, ... - _R. J. Mathar_, Aug 10 2012
%H Vincenzo Librandi, <a href="/A015541/b015541.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,7).
%F a(n) = 5*a(n-1) + 7*a(n-2).
%t Join[{a=0,b=1},Table[c=5*b+7*a;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011 *)
%t LinearRecurrence[{5, 7}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 13 2012 *)
%o (Sage) [lucas_number1(n,5,-7) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 24 2009
%o (Magma) [n le 2 select n-1 else 5*Self(n-1) + 7*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 13 2012 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-7*x^2))) \\ _G. C. Greubel_, Jan 24 2018
%Y Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015443, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226.
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
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