A109532 a(n)= +a(n-3) +2*a(n-6) +a(n-9).

1, 1, 1, 1, 3, 1, 3, 6, 3, 6, 13, 6, 13, 28, 13, 28, 60, 28, 60, 129, 60, 129, 277, 129, 277, 595, 277, 595, 1278, 595, 1278, 2745, 1278, 2745, 5896, 2745, 5896, 12664, 5896, 12664, 27201, 12664, 27201, 58425, 27201, 58425, 125491, 58425, 125491, 269542

Offset

0,5

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+x^2+2*x^4+x^7)/(1-x^3-2*x^6-x^9).

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][[2]], {n, 0, 100}]

Crossrefs

Cf. A000931, A109531, A109533.

Sequence in context: A359937 A255974 A033789 * A264584 A137338 A176106

Adjacent sequences: A109529 A109530 A109531 * A109533 A109534 A109535

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 18 2005

Extensions

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

Status

approved