%I #48 Oct 25 2023 10:00:27

%S 0,1,9,89,873,8569,84105,825497,8102313,79524793,780541641,7661073113,

%T 75193991145,738034505209,7243862476041,71099038326041,

%U 697842244742697,6849372509292601,67227090541574985,659838794948515673,6476365878869240937,63566003269411293817

%N Expansion of g.f. x/(1 - 9*x - 8*x^2).

%C Pisano period lengths: 1, 1, 4, 1, 24, 4, 6, 1, 4, 24, 10, 4, 12, 6, 24, 1,144, 4, 15, 24, ... . - _R. J. Mathar_, Aug 10 2012

%H Vincenzo Librandi, <a href="/A015584/b015584.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 (9,8).

%F a(n) = 9*a(n-1) + 8*a(n-2).

%F a(n) = (-((9-sqrt(113))/2)^n + ((9+sqrt(113))/2)^n) / sqrt(113). - _Colin Barker_, May 16 2017

%F E.g.f.: 2*exp(9*x/2)*sinh(sqrt(113)*x/2)/sqrt(113). - _Stefano Spezia_, Oct 25 2023

%t LinearRecurrence[{9, 8}, {0, 1}, 30] (* _Vincenzo Librandi_, Nov 15 2012 *)

%t CoefficientList[Series[x/(1-9x-8x^2),{x,0,30}],x] (* _Harvey P. Dale_, Sep 06 2022 *)

%o (Sage) [lucas_number1(n,9,-8) for n in range(0, 19)] # _Zerinvary Lajos_, Apr 26 2009

%o (Magma) [n le 2 select n-1 else 9*Self(n-1) + 8*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 15 2012

%o (PARI) concat(0, Vec(x / (1-9*x-8*x^2) + O(x^30))) \\ _Colin Barker_, May 16 2017

%Y Cf. A015579, A099371.

%K nonn,easy

%O 0,3

%A _Olivier Gérard_

%E Extended by _T. D. Noe_, May 23 2011