A107856 a(n) = 2*a(n-2)+4*a(n-4)+a(n-6), n>9.

1, 1, 1, 0, 4, 4, 11, 7, 37, 30, 122, 92, 403, 311, 1331, 1020, 4396, 3376, 14519, 11143, 47953, 36810, 158378, 121568, 523087, 401519, 1727639, 1326120, 5706004, 4379884, 18845651, 14465767, 62242957, 47777190, 205574522, 157797332

Offset

1,5

Links

Table of n, a(n) for n=1..36.

Formula

Limit_{n->infinity} a(n)/a(n-1) alternates between 0.767592... and 4.3027...

G.f.: x*(1+x+x^2)*(2*x^6+2*x^2-1)/( (1+x^2)*(x^4+3*x^2-1)) [Sep 28 2009]

Mathematica

M[n_] := If [Mod[n, 2] == 0, {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 3, 0, -3}}, {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, 1, 1}}] v[1] = {1, 1, 1, 0} v[n_] := v[n] = M[n].v[n - 1] a0 = Table[Abs[v[n][[1]]], {n, 1, 50}]

Crossrefs

Sequence in context: A343090 A161433 A180498 * A212102 A168373 A266438

Adjacent sequences: A107853 A107854 A107855 * A107857 A107858 A107859

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 12 2005

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

Status

approved