A109531 - OEIS

%I #9 Apr 10 2022 13:00:07

%S 0,1,1,1,1,4,1,3,7,3,6,16,6,13,34,13,28,73,28,60,157,60,129,337,129,

%T 277,724,277,595,1555,595,1278,3340,1278,2745,7174,2745,5896,15409,

%U 5896,12664,33097,12664,27201,71089,27201,58425,152692,58425,125491,327967

%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).

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,2,0,0,1).

%F G.f.: -x*(x^2-x+1)*(x^5+x^4+2*x^2+2*x+1)/(-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][[1]], {n, 0, 100}]

%t LinearRecurrence[{0,0,1,0,0,2,0,0,1},{0,1,1,1,1,4,1,3,7},70] (* _Harvey P. Dale_, Apr 10 2022 *)

%Y Cf. A000931, A109532, A109533.

%K nonn,easy

%O 0,6

%A _Roger L. Bagula_, Jun 18 2005

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