login
Number of n-length words on {1,2,3,4,5} such that the maximal runs of identical odd integers are of odd length and the maximal runs of identical even integers are of even length.
2

%I #12 Jun 13 2015 00:55:02

%S 1,3,8,27,82,255,794,2463,7654,23775,73850,229407,712606,2213583,

%T 6876098,21359343,66348934,206100927,640215146,1988712255,6177573934,

%U 19189513071,59608742162,185163746895,575177598550,1786684895967,5550012597050,17240107585311,53553267556606,166353513271311,516747019188962

%N Number of n-length words on {1,2,3,4,5} such that the maximal runs of identical odd integers are of odd length and the maximal runs of identical even integers are of even length.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,2,-2).

%F G.f.: (1 + x - x^2)/(1 - 2*x - 3*x^2 - 2*x^3 + 2*x^4).

%F a(n) = 2*a(n-1) +3*a(n-2) +2*a(n-3) -2*a(n-4). - _Fung Lam_, May 18 2014

%e a(3)=27 because we have: 111, 122, 131, 135, 144, 151, 153, 221, 223, 225, 313, 315, 322, 333, 344, 351, 353, 441, 443, 445, 513, 515, 522, 531, 535, 544, 555.

%t n=5;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]

%Y Cf. A062200, A242510, A242536.

%K nonn,easy

%O 0,2

%A _Geoffrey Critzer_, May 17 2014