A109533 a(n) = a(n-3) + 2*a(n-6) + a(n-9).

1, 0, 1, 2, 1, 3, 5, 1, 6, 10, 3, 13, 22, 6, 28, 47, 13, 60, 101, 28, 129, 217, 60, 277, 466, 129, 595, 1001, 277, 1278, 2150, 595, 2745, 4618, 1278, 5896, 9919, 2745, 12664, 21305, 5896, 27201, 45761, 12664, 58425, 98290, 27201, 125491, 211117, 58425

Offset

0,4

Comments

The recurrence shows that these are actually three interleaved sequences with the same recurrence (and the same characteristic polynomial).

Links

Table of n, a(n) for n=0..49.

Formula

G.f.: (1+x^2+x^3+x^4+2*x^5+x^6+x^8)/(1-x^3-2*x^6-x^9). [Sep 28 2009]

Mathematica

M1 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}; M2 = {{0, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M3 = {{0, 1, 0}, {1, 0, 1}, {1, 0, 0}}; M[n_] = If[Mod[n, 3] == 1, M3, If[Mod[n, 3] == 2, M2, M1]]; v[0] = {0, 1, 1}; v[n_] := v[n] = M[n].v[n - 1] a = Table[v[n][[3]], {n, 0, 100}]

Crossrefs

Cf. A000931, A109531, A109523.

Sequence in context: A215564 A189449 A239286 * A062705 A059234 A120852

Adjacent sequences: A109530 A109531 A109532 * A109534 A109535 A109536

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 18 2005

Extensions

New name from the Associate Editors of the OEIS, Sep 28 2009

Status

approved