A109529 - OEIS

%I #4 Mar 30 2012 17:34:19

%S 1,2,1,2,9,2,9,34,9,34,131,34,131,504,131,504,1939,504,1939,7460,1939,

%T 7460,28701,7460,28701,110422,28701,110422,424829,110422,424829,

%U 1634454,424829,1634454,6288271,1634454,6288271,24193004,6288271,24193004

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

%C The recurrence shows that these are actually three interleaved sequences with

%C the same recurrence (and the same characteristic polynomial).

%F 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]

%t 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}]

%Y Cf. A000213, A109528, A109530.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Jun 18 2005

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