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%I #25 Feb 19 2021 01:53:03
%S 0,1,2,5,11,23,46,89,168,311,567,1021,1820,3217,5646,9849,17091,29523,
%T 50794,87081,148820,253611,431087,731065,1237176,2089633,3523226,
%U 5930669,9968123,16730831,28045222,46954361,78524160,131181407
%N a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-2) + a(n-1) + A000071(n+1).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,1,1).
%F From _R. J. Mathar_, Apr 27 2010: (Start)
%F a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).
%F G.f.: -x*(1 - x + x^3) / ( (x - 1)*(x^2 + x - 1)^2 ). (End)
%F a(n) = A140998(n+1, k = 2) = A140993(n+2, n) for n >= 1. - _Petros Hadjicostas_, Jun 10 2019
%e If n = 4, then a(4) = a(4-2) + a(4-1) + A000071(4+1) = a(2) + a(3) + A000071(5) = 2 + 5 + 4 = 11.
%t LinearRecurrence[{3,-1,-3,1,1},{0,1,2,5,11},40] (* _Harvey P. Dale_, Jun 12 2014 *)
%Y Cf. A000071, A000045, A140993, A140998.
%K nonn,easy
%O 0,3
%A _Juri-Stepan Gerasimov_, Jul 08 2008
%E Corrected (5980669 replaced by 5930669) by _R. J. Mathar_, Apr 27 2010
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