A109530 a(n)= 3*a(n-3) +3*a(n-6) +a(n-9).

1, 0, 2, 6, 1, 9, 23, 2, 34, 88, 9, 131, 339, 34, 504, 1304, 131, 1939, 5017, 504, 7460, 19302, 1939, 28701, 74261, 7460, 110422, 285706, 28701, 424829, 1099203, 110422, 1634454, 4228988, 424829, 6288271, 16270279, 1634454, 24193004, 62597004

Offset

0,3

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.

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

Formula

G.f.: (1+2*x^2+3*x^3+x^4+3*x^5+2*x^6-x^7+x^8)/(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][[3]], {n, 0, 100}]
LinearRecurrence[{0, 0, 3, 0, 0, 3, 0, 0, 1}, {1, 0, 2, 6, 1, 9, 23, 2, 34}, 60] (* Harvey P. Dale, Sep 13 2022 *)

Crossrefs

Cf. A000213, A109529 A109528.

Sequence in context: A291836 A100831 A136763 * A264789 A111519 A184941

Adjacent sequences: A109527 A109528 A109529 * A109531 A109532 A109533

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