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A234284
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Number of 321-avoiding extensions of comb K_{s,3}^{beta}.
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0
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1, 10, 127, 1866, 29839, 504265, 8859742, 160216631, 2962451668, 55752953619, 1064455517286, 20566756704300, 401392396922394, 7901356125281267, 156695640175228660, 3127700524615849499, 62787047960901808378, 1266812106374162802049, 25675382888225888374354
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OFFSET
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1,2
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LINKS
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FORMULA
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Define F_{2,3}(k)=1 if 2<=k<=4 and 0 otherwise. For s>=3, let F_{s,3}(k) = Sum_{i=(s-1)..(k-1)} (F_{s-1,3}(i)*Sum_{j=(k-3s+4)..2} (binomial(k-i-1,j))). Then a(n) = Sum_{k=n..(3n-2)} (binomial(3n-k,2)*F_{n,3}(k)). - Colin Defant, Aug 16 2016
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MATHEMATICA
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F[1, 3][1] = 1;
F[2, 3][k_] := If[2 <= k <= 4, 1, 0 ];
F[s_ /; s >= 3, 3][k_] := F[s, 3][k] = Sum[F[s - 1, 3][i] Sum[Binomial[k - i - 1, j], {j, k - 3s + 4, 2}], {i, s - 1, k - 1}];
a[n_] := Sum[Binomial[3n - k, 2] F[n, 3][k], {k, n, 3n - 2}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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