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A274842
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Number of set partitions of [n] such that the difference between each element and its block index is a multiple of nine.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 42, 81, 152, 279, 502, 885, 1524, 2547, 6629, 15815, 35713, 77769, 165155, 344379, 707693, 1434461, 2859871, 8415994, 23485835, 62727630, 161710529, 404995340, 989816263, 2367377650, 5547588797
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OFFSET
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0,11
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LINKS
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EXAMPLE
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a(9) = 1: 1|2|3|4|5|6|7|8|9.
a(10) = 2: 1(10)|2|3|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).
a(11) = 3: 1(10)|2(11)|3|4|5|6|7|8|9, 1|2(11)|3|4|5|6|7|8|9|(10), 1|2|3|4|5|6|7|8|9|(10)|(11).
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MAPLE
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b:= proc(n, m, t) option remember; `if`(n=0, 1,
add(`if`(irem(j-t, 9)=0, b(n-1, max(m, j),
irem(t+1, 9)), 0), j=1..m+1))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..45);
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MATHEMATICA
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b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 9] == 0, b[n - 1, Max[m, j], Mod[t + 1, 9]], 0], {j, 1, m + 1}]];
a[n_] := b[n, 0, 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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STATUS
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approved
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