%I A109530
%S A109530 1,0,2,6,1,9,23,2,34,88,9,131,339,34,504,1304,131,1939,5017,504,7460,
%T A109530 19302,1939,28701,74261,7460,110422,285706,28701,424829,1099203,110422,
%U A109530 1634454,4228988,424829,6288271,16270279,1634454,24193004,62597004
%N A109530 a(n)= 3*a(n-3) +3*a(n-6) +a(n-9).
%C A109530 The recurrence shows that these are actually three interleaved sequences 
               with
%C A109530 the same recurrence (and the same characteristic polynomial).
%F A109530 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]
%t A109530 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}]
%Y A109530 Cf. A000213, A109529 A109528.
%Y A109530 Sequence in context: A011041 A100831 A136763 this_sequence A111519 A008855 
               A132181
%Y A109530 Adjacent sequences: A109527 A109528 A109529 this_sequence A109531 A109532 
               A109533
%K A109530 nonn,easy
%O A109530 0,3
%A A109530 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2005
%E A109530 Definition replaced by recurrence by the Associate Editors of the OEIS, 
               Sep 28 2009