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A242536
Number of n-length words on {1,2,3,4} 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, 2, 4, 12, 26, 66, 160, 386, 946, 2292, 5582, 13578, 33016, 80330, 195370, 475236, 1155974, 2811762, 6839416, 16636178, 40466002, 98429844, 239421374, 582370554, 1416562360, 3445657082, 8381242522, 20386597380, 49588514390, 120619477410, 293395730296
OFFSET
0,2
FORMULA
G.f.: (1 + x - x^2)/(1 - x -3*x^2 - 2*x^3 + 2*x^4).
a(n) = a(n-1) +3*a(n-2) +2*a(n-3) -2*a(n-4). - Fung Lam, May 18 2014
EXAMPLE
a(3)=12 because we have: 111, 122, 131, 144, 221, 223, 313, 322, 333, 344, 441, 443.
MATHEMATICA
n=4; 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