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A133592 a(n) = 2*a(n-1)+6*a(n-2) for n>=3, a(0)=1, a(1)=2, a(2)=8.

%I A133592 #23 Jul 01 2023 09:17:25
%S A133592 1,2,8,28,104,376,1376,5008,18272,66592,242816,885184,3227264,
%T A133592 11765632,42894848,156383488,570136064,2078573056,7577962496,
%U A133592 27627363328,100722501632,367209183232,1338753376256,4880761851904,17794043961344
%N A133592 a(n) = 2*a(n-1)+6*a(n-2) for n>=3, a(0)=1, a(1)=2, a(2)=8.
%H A133592 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,6).
%F A133592 G.f.: (1-2*x^2)/(1-2*x-6*x^2).
%F A133592 a(n) = Sum_{k=0..n} A122950(n,k)*2^k .
%F A133592 a(n) = ((7+2*sqrt(7))/21)*(1+sqrt(7))^n+((7-2*sqrt(7))/21)*(1-sqrt(7))^n for n=>1. [_Richard Choulet_, Nov 19 2008]
%F A133592 a(n) = A083099(n+1) - 2*A083099(n-1). - _R. J. Mathar_, Jun 20 2015
%p A133592 A133592 := proc(n)
%p A133592         option remember;
%p A133592         if n <=1 then
%p A133592                 n+1;
%p A133592         elif n = 2 then
%p A133592                 8;
%p A133592         else
%p A133592                 2*procname(n-1)+6*procname(n-2) ;
%p A133592         fi ;
%p A133592 end proc: # _R. J. Mathar_, Jul 15 2017
%t A133592 Join[{1}, LinearRecurrence[{2, 6}, {2, 8}, 24]] (* _Jean-François Alcover_, Jul 01 2023 *)
%Y A133592 Cf. A083099, A122950.
%K A133592 easy,nonn
%O A133592 0,2
%A A133592 _Philippe Deléham_, Dec 31 2007
%E A133592 a(16) corrected by _R. J. Mathar_, Jun 20 2015