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A242510 Number of n-length words on {1,2,3} such that the maximal blocks (runs) of 1's have odd length, the maximal blocks of 2's have even length and the maximal blocks of 3's have odd length.

%I A242510 #18 Jun 13 2015 00:55:02
%S A242510 1,2,3,8,15,32,67,138,289,600,1249,2600,5409,11258,23427,48752,101455,
%T A242510 211128,439363,914322,1902721,3959600,8240001,17147600,35684481,
%U A242510 74260082,154536643,321593688,669242575,1392706512,2898248707
%N A242510 Number of n-length words on {1,2,3} such that the maximal blocks (runs) of 1's have odd length, the maximal blocks of 2's have even length and the maximal blocks of 3's have odd length.
%H A242510 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,1,-1).
%F A242510 G.f.: (1 + x - x^2)/(1 - x - 2*x^2 - x^3 +x^4).
%F A242510 a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4). - _Fung Lam_, May 18 2014
%e A242510 a(3)=8 because we have: 111, 122, 131, 221, 223, 313, 322, 333.
%t A242510 n=3;nn=30;CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i]),{i,1,n}])/.Join[Table[v[i]->z/(1-z^2),{i,1,n,2}],Table[v[i]->z^2/(1-z^2),{i,2,n,2}]],{z,0,nn}],z]
%t A242510 (* Changing n=3 at the beginning of this code to n = k, (for k a positive integer) will return the number of n-length words on {1,2,...,k} where the maximal run lengths of odd integers are odd and the maximal run lengths of even integers are even. *)
%Y A242510 Cf. A062200, A242536, A242537.
%K A242510 nonn
%O A242510 0,2
%A A242510 _Geoffrey Critzer_, May 16 2014