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A242510
Number of n-length words on {1,2,3} such that the maximal blocks (runs) of 1's have odd length, the maximal blocks of 2's have even length and the maximal blocks of 3's have odd length.
2
1, 2, 3, 8, 15, 32, 67, 138, 289, 600, 1249, 2600, 5409, 11258, 23427, 48752, 101455, 211128, 439363, 914322, 1902721, 3959600, 8240001, 17147600, 35684481, 74260082, 154536643, 321593688, 669242575, 1392706512, 2898248707
OFFSET
0,2
FORMULA
G.f.: (1 + x - x^2)/(1 - x - 2*x^2 - x^3 +x^4).
a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4). - Fung Lam, May 18 2014
EXAMPLE
a(3)=8 because we have: 111, 122, 131, 221, 223, 313, 322, 333.
MATHEMATICA
n=3; 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]
(* Changing n=3 at the beginning of this code to n = k, (for k a positive integer) will return the number of n-length words on {1, 2, ..., k} where the maximal run lengths of odd integers are odd and the maximal run lengths of even integers are even. *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 16 2014
STATUS
approved