A107840 a(n)= 3*a(n-1) -3*a(n-3) +a(n-4), n>6.

1, 1, 1, 0, 4, 8, 25, 63, 169, 440, 1156, 3024, 7921, 20735, 54289, 142128, 372100, 974168, 2550409, 6677055, 17480761, 45765224, 119814916, 313679520, 821223649, 2149991423, 5628750625, 14736260448, 38580030724, 101003831720

Offset

1,5

Links

Table of n, a(n) for n=1..30.

Formula

lim a(n)/a(n-1) = 1+(Sqrt[5]+1)/2.

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

a(n) = -1/2-9*(-1)^n/10 +7*A001906(n+1)/5 -18*A001906(n)/5, n>2 [Sep 28 2009]

Mathematica

(* method one*) F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 0; F[n__] := F[n] = -3*F[n - 1] + 3*F[n - 3] + F[n - 4] a = Table[Abs[F[n]], {n, 1, 50}] an = Table[N[a[[n]]/a[[n - 1]]], {n, 6, 25}] (* method two*) M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 3, 0, -3}} v[1] = {1, 1, 1, 0} v[n_] := v[n] = M.v[n - 1] a0 = Table[Abs[v[n][[1]]], {n, 1, 50}] an = Table[N[a0[[n]]/a0[[n - 1]]], {n, 6, 25}] Det[M - x*IdentityMatrix[4]]

Crossrefs

Sequence in context: A000964 A297458 A328038 * A046736 A174171 A262042

Adjacent sequences: A107837 A107838 A107839 * A107841 A107842 A107843

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