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A331623
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Number of sequences with n copies each of 1,2,...,n avoiding absolute differences between adjacent elements larger than one.
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2
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1, 1, 6, 92, 11482, 8956752, 54331653686, 2535604038015218, 951645881858020642746, 2911820015993491302722966990, 73784388170659542104264761249115686, 15642058800086197220958447712819197014917632, 27980772370697320617389378491983217784996780441605354
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 1: the empty sequence.
a(1) = 1: 1.
a(2) = 6: 1122, 1212, 1221, 2112, 2121, 2211.
a(3) = 92: 111222333, 111223233, 111223323, 111223332, ..., 333221112, 333221121, 333221211, 333222111.
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MAPLE
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b:= proc(l, q) option remember; (n-> `if`(n<2, 1, add(
`if`(l[j]=1, `if`(j in [1, n], b(subsop(j=[][], l),
`if`(j=1, 0, n)), 0), b(subsop(j=l[j]-1, l), j)), j=
`if`(q<0, 1..n, max(1, q-1)..min(n, q+1)))))(nops(l))
end:
a:= n-> b([n$n], -1):
seq(a(n), n=0..6);
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MATHEMATICA
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b[l_, q_] := b[l, q] = With[{n = Length[l]}, If[n < 2, 1, Sum[
If[l[[j]] == 1, If[j == 1 || j == n, b[ReplacePart[l, j -> Nothing],
If[j == 1, 0, n]], 0], b[ReplacePart[l, j -> l[[j]] - 1], j]], {j,
If[q < 0, Range[n], Range[Max[1, q - 1], Min[n, q + 1]]]}]]];
a[n_] := b[Table[n, {n}], -1];
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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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