A115108 Expansion of -(9520*x^9 -11504*x^8 +2840*x^7 -1040*x^6 +248*x^5 +36*x^4 -1) / ((2*x -1)*(4*x^2 +2*x -1)).

1, 4, 16, 56, 156, 248, 1584, 2248, 18512, 51856, 189440, 609664, 2023808, 6579712, 21441536, 69575680, 225665024, 731127808, 2367905792, 7666302976, 24816189440, 80321511424, 259955621888, 841292972032, 2722599796736

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (4,0,-8).

Formula

G.f.: -(9520*x^9 -11504*x^8 +2840*x^7 -1040*x^6 +248*x^5 +36*x^4 -1) / ((2*x -1)*(4*x^2 +2*x -1)). - Colin Barker, Mar 15 2013

a(n) = +4*a(n-1) -8*a(n-3). - Colin Barker, Mar 15 2013

Mathematica

M0 = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; M1 = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; M2 = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; M[n_] := M[n] = If[Mod[v[n][[1]], 3] == 0, M1, If[Mod[v[n][[2]], 3] == 0, M0, M2]] v[0] = {1, 1, 1}; M[0] = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; v[n_] := v[n] = M[n - 1].v[n - 1] a0 = Table[v[n][[1]], {n, 0, 25}]

Crossrefs

Sequence in context: A288187 A333282 A212520 * A127393 A239988 A308288

Adjacent sequences: A115105 A115106 A115107 * A115109 A115110 A115111

Keyword

nonn,easy,less

Author

Roger L. Bagula, Mar 03 2006

Extensions

Explicit name by Joerg Arndt, Mar 15 2013

Status

approved