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Expansion of x/(1 - 9*x - 11*x^2).
2

%I #36 Dec 18 2023 10:05:05

%S 0,1,9,92,927,9355,94392,952433,9610209,96968644,978430095,9872525939,

%T 99615464496,1005136965793,10142002801593,102334531838060,

%U 1032572817360063,10418835206459227,105127817849093736,1060757547912895121,10703223927556087185,107997348375046630996

%N Expansion of x/(1 - 9*x - 11*x^2).

%C Pisano period lengths: 1, 3, 4, 6, 20, 12, 48, 6, 12, 60, 5, 12,168, 48, 20, 12,288, 12, 6, 60,... - _R. J. Mathar_, Aug 10 2012

%H Vincenzo Librandi, <a href="/A015587/b015587.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 (9,11).

%F a(n) = 9*a(n-1) + 11*a(n-2).

%t Join[{a=0,b=1},Table[c=9*b+11*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 29 2011 *)

%t LinearRecurrence[{9, 11}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 15 2012 *)

%o (Sage) [lucas_number1(n,9,-11) for n in range(0, 19)] # _Zerinvary Lajos_, Apr 26 2009

%o (Magma) [n le 2 select n-1 else 9*Self(n-1) + 11*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2012

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-11*x^2))) \\ _G. C. Greubel_, Jan 06 2018

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_