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a(n) = a(n-1)+9*a(n-2) initialized with a(0)=1, a(1)=3.
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%I #30 Jun 13 2015 00:52:09

%S 1,3,12,39,147,498,1821,6303,22692,79419,283647,998418,3551241,

%T 12537003,44498172,157331199,557814747,1973795538,6994128261,

%U 24758288103,87705442452,310530035379,1099879017447,3894649335858,13793560492881,48845404515603,172987448951532

%N a(n) = a(n-1)+9*a(n-2) initialized with a(0)=1, a(1)=3.

%C The two roots of the denominator of the g.f. (for Binet's formula) are -0.393486... and 0.2823756...

%C Pisano period lengths: 1, 3, 1, 6, 6, 3, 6, 12, 1, 6, 10, 6, 84, 6, 6, 24,144, 3, 72, 6,... - _R. J. Mathar_, Aug 10 2012

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,9).

%F G.f.: -(1+2*x)/(-1+x+9*x^2). a(n) = A015445(n)+2*A015445(n-1). [_R. J. Mathar_, Aug 12 2009]

%F a(n) = (1/2+5*sqrt(37)/74) *(1/2+sqrt(37)/2)^(n-1) +(1/2-5*sqrt(37)/74) *(1/2-sqrt(37)/2)^(n-1). [_Antonio Alberto Olivares_, Jun 07 2011]

%F a(n) = Sum_{k, 0<=k<=n} A103631(n,k)*3^k. - _Philippe Deléham_, Dec 17 2011

%F a(n) = A015445(n) + 2*A015445(n-1), n>0. - _Ralf Stephan_, Jul 21 2013

%t CoefficientList[Series[(-2 z - 1)/(9 z^2 + z - 1), {z, 0, 200}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 11 2011 *)

%Y Cf. A026597.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Sep 22 2006

%E Definition replaced with the Deleham recurrence of Mar 2009 by the Assoc. Editors of the OEIS, Mar 12 2010