login
a(n+5) = (-8 + 5*n)*a(n-1) + (72 - 20*n)*a(n) + (-146 + 21*n)*a(n+1) + (128 - 8*n)*a(n+2) + (-56 + n)*a(n+3) + 12*a(n+4).
0

%I #18 Nov 14 2018 09:33:54

%S 1,12,90,548,2986,15284,74309,346716,1571119,6992940,30875360,

%T 136381936,607183046,2742567784,12641133025,59750365748,290733288513,

%U 1460096920092,7578070997402,40648251605280,225116682011442

%N a(n+5) = (-8 + 5*n)*a(n-1) + (72 - 20*n)*a(n) + (-146 + 21*n)*a(n+1) + (128 - 8*n)*a(n+2) + (-56 + n)*a(n+3) + 12*a(n+4).

%F For n >= 1, a(n+5) = (-8 + 5*n)*a(n-1) + (72 - 20*n)*a(n) + (-146 + 21*n)*a(n+1) + (128 - 8*n)*a(n+2) + (-56 + n)*a(n+3) + 12*a(n+4). - _Jianing Song_, Nov 10 2018

%t M[n_] := {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, -1*{8 - 5 n, -72 + 20 n, 146 - 21 n, -128 + 8 n, 56 - n, -12}};

%t v[0] = {1, 12, 90, 548, 2986, 15284};

%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, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -8 + 5*n, 72 - 20*n, -146 + 21*n, 128 - 8*n, -56 + n, 12];

%o T(n) = if(n==0, [1; 12; 90; 548; 2986; 15284], M(n)*T(n-1))

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

%K nonn,easy,less

%O 0,2

%A _Roger L. Bagula_, Jun 16 2007

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