A242537 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.
1, 3, 8, 27, 82, 255, 794, 2463, 7654, 23775, 73850, 229407, 712606, 2213583, 6876098, 21359343, 66348934, 206100927, 640215146, 1988712255, 6177573934, 19189513071, 59608742162, 185163746895, 575177598550, 1786684895967, 5550012597050, 17240107585311, 53553267556606, 166353513271311, 516747019188962
Offset: 0
Examples
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.
Links
- Index entries for linear recurrences with constant coefficients, signature (2,3,2,-2).
Programs
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Mathematica
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]
Formula
G.f.: (1 + x - x^2)/(1 - 2*x - 3*x^2 - 2*x^3 + 2*x^4).
a(n) = 2*a(n-1) +3*a(n-2) +2*a(n-3) -2*a(n-4). - Fung Lam, May 18 2014