A122012 G.f.: x^2*(3+3*x-2*x^2)/ ( (x^2-x-1) * (x^2+x-1)).

0, 3, 3, 7, 9, 18, 24, 47, 63, 123, 165, 322, 432, 843, 1131, 2207, 2961, 5778, 7752, 15127, 20295, 39603, 53133, 103682, 139104, 271443, 364179, 710647, 953433, 1860498, 2496120, 4870847, 6534927, 12752043, 17108661, 33385282, 44791056

Offset: 1

Author

Roger L. Bagula, Sep 11 2006

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, -1).

Programs

Mathematica

M = {{0, 1, 1, 0}, {1, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}} v[1] = {0, 1, 2, 3} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]

Formula

a(n)= 3*a(n-2) -a(n-4).

a(n)= A022096(n-1)/2 + (-1)^n*A000045(n-2)/2, n >1.

a(2n+1)= A099256(2n-2), n>=1. [Mar 27 2010]

Extensions

Definition replaced with generating function by the Assoc. Eds. of the OEIS, Mar 27 2010