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

%I #8 Feb 02 2017 02:41:52

%S 1,0,1,2,1,3,5,1,6,10,3,13,22,6,28,47,13,60,101,28,129,217,60,277,466,

%T 129,595,1001,277,1278,2150,595,2745,4618,1278,5896,9919,2745,12664,

%U 21305,5896,27201,45761,12664,58425,98290,27201,125491,211117,58425

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

%C The recurrence shows that these are actually three interleaved sequences with the same recurrence (and the same characteristic polynomial).

%F G.f.: (1+x^2+x^3+x^4+2*x^5+x^6+x^8)/(1-x^3-2*x^6-x^9). [Sep 28 2009]

%t 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][[3]], {n, 0, 100}]

%Y Cf. A000931, A109531, A109523.

%K nonn,easy

%O 0,4

%A _Roger L. Bagula_, Jun 18 2005

%E New name from the Associate Editors of the OEIS, Sep 28 2009