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A242495
Number of length n words on {1,2,3,4} with at most one consecutive 1 and at most two consecutive 2's and at most three consecutive 3's and at most four consecutive 4's.
3
1, 4, 15, 56, 208, 773, 2872, 10672, 39655, 147350, 547523, 2034486, 7559742, 28090486, 104378617, 387850022, 1441172953, 5355109869, 19898515060, 73938894118, 274742112508, 1020886629235, 3793410119173, 14095551768590
OFFSET
0,2
COMMENTS
Column k=4 of A242464.
LINKS
FORMULA
G.f.: (1 + x)*(1 + x^2)*(1 + x + x^2 )*(1 + x + x^2 + x^3 + x^4)/(1 - x - 5*x^2 - 12*x^3 - 18*x^4 - 22*x^5 - 20*x^6 - 15*x^7 - 8*x^8 - 3*x^9). (corrected by Fung Lam, May 18 2014)
EXAMPLE
a(3) = 56 because there are 64 length 3 words on {1,2,3,4} but we don't count 111, 112, 113, 114, 211, 222, 311, or 411.
MATHEMATICA
nn=23; CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i])/.v[i]->(z-z^(i+1))/(1-z), {i, 1, 4}]), {z, 0, nn}], z]
CROSSREFS
Cf. A242452.
Sequence in context: A291030 A217779 A191606 * A221859 A106707 A125905
KEYWORD
nonn,easy
AUTHOR
Geoffrey Critzer, May 16 2014
STATUS
approved