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A287252
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Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks are <= two.
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4
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1, 1, 2, 5, 14, 44, 152, 571, 2317, 10096, 47013, 232944, 1223428, 6786936, 39640947, 243060305, 1560340480, 10461611439, 73094563140, 531127372268, 4006242743228, 31316162403165, 253292622192153, 2116823651781702, 18255325000268015, 162261535224570326
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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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MAPLE
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b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
`if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
end:
a:= n-> b(n-1, min(2, n-1), 1, n):
seq(a(n), n=0..30);
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MATHEMATICA
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b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m*b[n - 1, k, m, l]];
a[n_] := b[n - 1, Min[2, n - 1], 1, n];
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CROSSREFS
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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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