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A328432
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Number of inversion sequences of length n avoiding the consecutive patterns 010, 021, and 120.
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15
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1, 1, 2, 5, 15, 53, 216, 994, 5076, 28403, 172538, 1129511, 7919314, 59150556, 468504022, 3919569708, 34518111783, 319030219223, 3086250047021, 31174921402976, 328110078110137, 3591110146030066, 40800503952916639, 480429785491094856, 5854374278697301978
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OFFSET
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0,3
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COMMENTS
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A length n inversion sequence e_1e_2...e_n is a sequence of integers such that 0 <= e_i < i. The term a(n) counts the inversion sequences of length n with no entries e_i, e_{i+1}, e_{i+2} such that e_i < e_{i+1} > e_{i+2}. This is the same as the set of inversion sequences of length n avoiding the consecutive patterns 010, 021, and 120.
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LINKS
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EXAMPLE
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The a(4)=15 length 4 inversion sequences avoiding the consecutive patterns 010, 021, 120 and are 0000, 0110, 0001, 0011, 0111, 0002, 0012, 0112, 0022, 0122, 0003, 0013, 0113, 0023, and 0123.
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MAPLE
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b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
`if`(t and i < x, 0, b(n - 1, i, i > x)), i = 0 .. n - 1))
end proc:
a := n -> b(n, n, false):
seq(a(n), n = 0 .. 24);
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MATHEMATICA
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b[n_, x_, t_] := b[n, x, t] = If[n == 0, 1, Sum[If[t && i < x, 0, b[n - 1, i, i > x]], {i, 0, n - 1}]];
a[n_] := b[n, n, False];
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CROSSREFS
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Cf. A328357, A328358, A328429, A328430, A328431, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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