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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.
2
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
0,2
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
EXAMPLE
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.
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]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Geoffrey Critzer, May 17 2014
STATUS
approved