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a(n+2) = 6*a(n+1) + (-11 + n)*a(n) + (6 - 2*n)*a(n-1) for n >= 1.
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%I #12 Oct 10 2018 12:52:02

%S 0,0,1,6,27,114,483,2106,9537,44934,219933,1115286,5842707,31537314,

%T 174991443,996169146,5808168297,34633891734,210943794093,

%U 1310837402646,8302614222507,53552183145234,351468155184003,2345436650546106

%N a(n+2) = 6*a(n+1) + (-11 + n)*a(n) + (6 - 2*n)*a(n-1) for n >= 1.

%F a(n+2) = 6*a(n+1) + (-11 + n)*a(n) + (6 - 2*n)*a(n-1) for n >= 1. \\ _Jianing Song_, Oct 10 2018

%t M[n_] := {{0, 1, 0}, {0, 0, 1}, {6 - 2*n, -11 + n, 6}}

%t v[0] = {0, 0, 1};

%t v[n_] := v[n] = M[n].v[n - 1]

%t a = Table[v[n][[1]], {n, 0, 30}]

%o (PARI) M(n) = [0, 1, 0; 0, 0, 1; 6 - 2*n, -11 + n, 6];

%o T(n) = if(n==0, [0; 0; 1], M(n)*T(n-1))

%o a(n) = T(n)[1, 1] \\ _Jianing Song_, Oct 10 2018

%K nonn,easy

%O 0,4

%A _Roger L. Bagula_, Jun 16 2007

%E Edited, new name, and offset corrected by _Jianing Song_, Oct 10 2018