A130592 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).

1, 12, 90, 548, 2986, 15284, 74309, 346716, 1571119, 6992940, 30875360, 136381936, 607183046, 2742567784, 12641133025, 59750365748, 290733288513, 1460096920092, 7578070997402, 40648251605280, 225116682011442

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Mathematica

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}};
v[0] = {1, 12, 90, 548, 2986, 15284};
v[n_] := v[n] = M[n].v[n - 1]
a = Table[v[n][[1]], {n, 0, 30}]

Prog

(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];
T(n) = if(n==0, [1; 12; 90; 548; 2986; 15284], M(n)*T(n-1))
a(n) = T(n)[1, 1] \\ Jianing Song, Nov 10 2018

Crossrefs

Sequence in context: A036216 A022640 A090749 * A002544 A093801 A273099

Adjacent sequences: A130589 A130590 A130591 * A130593 A130594 A130595

Keyword

nonn,easy,less

Author

Roger L. Bagula, Jun 16 2007

Extensions

Edited, new name, and offset corrected by Jianing Song, Nov 10 2018

Status

approved