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%I #21 Jan 14 2023 17:05:05
%S -1,3,7,27,95,339,1207,4299,15311,54531,194215,691707,2463551,8774067,
%T 31249303,111296043,396386735,1411752291,5028030343,17907595611,
%U 63778847519,227151733779,809012896375,2881342156683,10262052262799,36548841101763,130170627830887,463609565696187,1651169952750335
%N G.f.: (-1+6*x)/(1-3*x-2*x^2).
%C Encountered during the analysis of a certain cellular automaton.
%H Vincenzo Librandi, <a href="/A246313/b246313.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 (3,2).
%F a(n) = 3*a(n-1) + 2*a(n-2) with a(0)=-1, a(1)=3.
%F a(n) = -(17+9*sqrt(17))/34*(3/2-sqrt(17)/2)^n+(-17+9*sqrt(17))/34*(3/2+sqrt(17)/2)^n. For n >= 3, a(n) = round(-17+9*sqrt(17))/34*(3/2+sqrt(17)/2)^n). - _Robert Israel_, Aug 27 2014
%F a(n) = 6*A007482(n-1)+A007482(n). - _R. J. Mathar_, Feb 27 2019
%p a:= LRETools[REtoproc](a(n)=3*a(n-1)+2*a(n-2),a(n),{a(0)=-1,a(1)=3}):
%p seq(a(i),i=0..100); # _Robert Israel_, Aug 27 2014
%t CoefficientList[Series[(6 x - 1)/(1 - 3 x - 2 x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 27 2014 *)
%o (Magma) I:=[-1,3]; [n le 2 select I[n] else 3*Self(n-1)+2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Aug 27 2014
%o (PARI) Vec((-1+6*x)/(1-3*x-2*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 02 2014
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Aug 26 2014
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