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A328442
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Number of inversion sequences of length n avoiding the consecutive pattern 210.
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16
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1, 1, 2, 6, 24, 118, 684, 4554, 34192, 285558, 2624496, 26315990, 285828324, 3342566724, 41869664320, 559265742918, 7934746600620, 119162454310392, 1888417811354292, 31492626988890798, 551302582228438512, 10107905106374914860, 193700015975819881008, 3872391687779493752340, 80623321999146782133372
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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}. That is, a(n) counts the inversion sequences of length n avoiding the consecutive pattern 210.
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LINKS
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FORMULA
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a(n) ~ n! * c * (3^(3/2)/(2*Pi))^n * n^(2*Pi/3^(3/2)), where c = 0.24427562500895080639039917229089... - Vaclav Kotesovec, Oct 19 2019
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EXAMPLE
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Note that a(5)=118. Indeed, of the 120 inversion sequences of length 5, the only ones that do not avoid the consecutive patterns 210 are 00210 and 01210.
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MAPLE
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b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
`if`(t and x < i, 0, b(n - 1, i, x < i)), 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 && x < i, 0, b[n - 1, i, x < i]], {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, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441.
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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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