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A242536
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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.
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2
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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EXAMPLE
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a(3)=12 because we have: 111, 122, 131, 144, 221, 223, 313, 322, 333, 344, 441, 443.
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MATHEMATICA
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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]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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