A108140 a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +a(n-4), n>8.

1, 1, 1, 1, 0, 4, 17, 55, 161, 449, 1220, 3266, 8667, 22879, 60203, 158107, 414728, 1087064, 2848061, 7459703, 19535229, 51152749, 133933964, 350666854, 918095255, 2403665279, 6292975607, 16475382935, 43133369616, 112925043724

Offset: 0

Author

Roger L. Bagula, Jun 05 2005

Keywords

• nonn
• easy

Links

• Roger Bagula, Factoring Double Fibonacci Sequences, 2000.
• Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).

Crossrefs

Cf. A000045, A056015, A056016.

Programs

Mathematica

F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 1; F[n__] := F[n] = 4*F[n - 1] - 3*F[n - 2] - 2*F[n - 3] + F[n - 4] a = Table[Abs[F[n]], {n, 1, 50}]

Formula

a(n) = -A000045(n+2)/2 + A001906(n-1)/2, n>3. [Sep 28 2009]

G.f.: (-1+2*x^7-2*x^6-8*x^5-2*x^3+3*x)/((x^2+x-1)*(x^2-3*x+1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

Extensions

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