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A274840
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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 seven.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 17, 34, 65, 120, 215, 374, 629, 1641, 3919, 8849, 19241, 40707, 84203, 170229, 503902, 1407019, 3746718, 9600121, 23815820, 57408783, 134592586, 440661179, 1383544922, 4206645985, 12456581554, 36012285385
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OFFSET
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0,9
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LINKS
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EXAMPLE
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a(8) = 2: 18|2|3|4|5|6|7, 1|2|3|4|5|6|7|8.
a(9) = 3: 18|29|3|4|5|6|7, 1|29|3|4|5|6|7|8, 1|2|3|4|5|6|7|8|9.
a(10) = 4: 18|29|3(10)|4|5|6|7, 1|29|3(10)|4|5|6|7|8, 1|2|3(10)|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).
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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, 7)=0, b(n-1, max(m, j),
irem(t+1, 7)), 0), j=1..m+1))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..42);
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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, 7] == 0, b[n - 1, Max[m, j], Mod[t + 1, 7]], 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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