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%I #17 Jul 31 2015 21:36:28
%S 1,5,14,44,128,392,1160,3512,10472,31544,94376,283640,849896,2551736,
%T 7651112,22961528,68868200,206637368,619846568,1859670776,5578750184,
%U 16736774840,50209275944,150629924984,451885580648,1355665130552
%N a(n)=a(n-1)+6a(n-2), n>2.
%C The binomial transform is A037481.
%C The recurrence of the definition is also satisfied by A087451, A102901 and A140725.
%H Vincenzo Librandi, <a href="/A140796/b140796.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 (1, 6).
%F a(n+1)-3a(n) = (-1)^n*A000079(n-1), n>0.
%F d(n+1)-3d(n) = (-1)^(n+1)*A000079(n-1), n>0, where d(n) is the sequence of pair sums d(n)= a(n)+a(n+1)=6, 19, 58, 172,...
%F O.g.f.: (1+x)(3x+1)/((2x+1)(1-3x)). - _R. J. Mathar_, Jul 29 2008
%F a(n) = (-1)^(n+1)*2^n/10+8*3^n/5, n>0. - _R. J. Mathar_, Jul 29 2008
%F a(n) = A140725(n)+A140725(n+1). - _Philippe Deléham_, Nov 17 2013
%t Join[{1},LinearRecurrence[{1,6},{5,14},30]] (* _Harvey P. Dale_, Nov 20 2011 *)
%Y Cf. A140725
%K nonn
%O 0,2
%A _Paul Curtz_, Jul 15 2008
%E Edited and extended by _R. J. Mathar_, Jul 29 2008
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