A130591 a(n+3) = (8 - 3*n)*a(n-1) + (-24 + 4*n)*a(n) + (22 - n)*a(n+1) - 8*a(n+2).

1, -8, 84, -836, 8617, -87016, 869799, -8590272, 83796504, -806946224, 7666848877, -71824221768, 662987321281, -6025366832504, 53867639536838, -473272010699496, 4081721963157687, -34511324853373512, 285631757521047043, -2309922250334330096, 18213524452315660914

Offset

0,2

Links

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

Formula

For n >= 1, a(n+3) = (8 - 3*n)*a(n-1) + (-24 + 4*n)*a(n) + (22 - n)*a(n+1) - 8*a(n+2). -- Jianing Song, Nov 10 2018

Mathematica

M[n_] := {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {8 - 3 n, -24 + 4 n, 22 - n, -8}};
v[0] ={1, -8, 84, -836};
v[n_] := v[n] = M[n].v[n - 1];
a = Table[v[n][[1]], {n, 0, 30}]
RecurrenceTable[{a[0]==1, a[1]==-8, a[2]==84, a[3]==-836, a[n+3]==(8-3n)a[n-1]+ (-24+4n)a[n]+(22-n)a[n+1]-8a[n+2]}, a, {n, 20}] (* Harvey P. Dale, Jun 19 2021 *)

Prog

(PARI) M(n) = [0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 8 - 3*n, -24 + 4*n, 22 - n, -8];
T(n) = if(n==0, [1; -8; 84; -836], M(n)*T(n-1))
a(n) = T(n)[1, 1] \\ Jianing Song, Nov 10 2018

Crossrefs

Sequence in context: A199907 A264710 A143868 * A166483 A048665 A005797

Adjacent sequences: A130588 A130589 A130590 * A130592 A130593 A130594

Keyword

sign,easy,less

Author

Roger L. Bagula, Jun 16 2007

Extensions

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

Status

approved