A109528 a(n)= 3*a(n-3) +3*a(n-6) +a(n-9).

0, 1, 3, 1, 2, 12, 2, 9, 45, 9, 34, 174, 34, 131, 669, 131, 504, 2574, 504, 1939, 9903, 1939, 7460, 38100, 7460, 28701, 146583, 28701, 110422, 563952, 110422, 424829, 2169705, 424829, 1634454, 8347554, 1634454, 6288271, 32115729, 6288271

Offset

0,3

Comments

The recurrence shows that this consists of three interleaved sequences (actually two, one doubled) with the same recurrence (and the same characteristic polynomial).

Links

Table of n, a(n) for n=0..39.

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

Formula

G.f.: x*(-1-3*x-x^2+x^3-3*x^4+x^5)/(-1+3*x^3+3*x^6+x^9). [From R. J. Mathar, Sep 27 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][[1]], {n, 0, 100}]
LinearRecurrence[{0, 0, 3, 0, 0, 3, 0, 0, 1}, {0, 1, 3, 1, 2, 12, 2, 9, 45}, 40] (* Harvey P. Dale, Mar 19 2013 *)

Crossrefs

Cf. A000931.

Sequence in context: A300546 A300973 A300930 * A136125 A092580 A004468

Adjacent sequences: A109525 A109526 A109527 * A109529 A109530 A109531

Keyword

nonn,easy

Author

Roger L. Bagula, Jun 18 2005

Extensions

Definition replaced by recurrence. - The Assoc. Editors of the OEIS, Oct 22 2009

Status

approved