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A328430
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Number of inversion sequences of length n avoiding the consecutive patterns 001 and 012.
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15
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1, 1, 2, 3, 7, 18, 70, 317, 1825, 11805, 88212, 727731, 6660103, 66377942, 718681969, 8376682083, 104703957902, 1395883946839, 19777652272297, 296686846198829, 4697959440255354, 78299282813403618, 1370127872827224359, 25114095425698971152, 481202765468970358153
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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 001 and 012.
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LINKS
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EXAMPLE
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The a(4)=7 length 4 inversion sequences avoiding the consecutive patterns 001 and 012 are 0000, 0100, 0110, 0101, 0111, 0102, and 0103.
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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, -1, 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, -1, False];
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CROSSREFS
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Cf. A328357, A328358, A328429, A328431, A328432, 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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