A109529 a(n)= 3*a(n-3) +3*a(n-6) +a(n-9).

1, 2, 1, 2, 9, 2, 9, 34, 9, 34, 131, 34, 131, 504, 131, 504, 1939, 504, 1939, 7460, 1939, 7460, 28701, 7460, 28701, 110422, 28701, 110422, 424829, 110422, 424829, 1634454, 424829, 1634454, 6288271, 1634454, 6288271, 24193004, 6288271, 24193004

Offset

0,2

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..39.

Formula

G.f.: (1+2*x+x^2-x^3+3*x^4-x^5+x^7)/(1-3*x^3-3*x^6-x^9). [Sep 28 2009]

Mathematica

M1 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}; M2 = {{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M3 = {{0, 1, 0}, {1, 1, 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. A000213, A109528, A109530.

Sequence in context: A188664 A326572 A119419 * A022694 A173159 A271574

Adjacent sequences: A109526 A109527 A109528 * A109530 A109531 A109532

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