A107855 a(n) = 2*a(n-2)+4*a(n-4)+a(n-6), n>11.

1, 1, 1, 0, 1, 1, 2, 3, 1, 10, 9, 33, 24, 109, 85, 360, 275, 1189, 914, 3927, 3013, 12970, 9957, 42837, 32880, 141481, 108601, 467280, 358679, 1543321, 1184642, 5097243, 3912601, 16835050, 12922449, 55602393, 42679944, 183642229, 140962285

Offset: 1

Author

Roger L. Bagula, Jun 12 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 4, 0, 1).

Programs

Mathematica

F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 0; F[n__] := F[n] = If[ Mod[n, 2] == 0, -3*F[n - 1] + 3*F[n - 3] + F[n - 4], F[n - 1] + F[n - 2]] a = Table[Abs[F[n]], {n, 1, 50}]
Join[{1,1,1,0,1},LinearRecurrence[{0,2,0,4,0,1},{1,2,3,1,10,9},50]] (* Harvey P. Dale, Oct 18 2013 *)

Formula

lim_{ n->inf} a(n)/a(n-1) alternating between 0.767592... and 4.30278...

G.f.: x*(2*x^10+8*x^8+5*x^6+3*x^5+5*x^4+x^2-1+2*x^3-x)/( (x^2+1)*(x^4+3*x^2-1)). [ Sep 28 2009]

a(2n) = A006190(n-2), a(2n+1) = (1/3)*[A052924(n-2) - 4*(-1)^n], n>2.

Extensions

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