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 A274842 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of nine. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..928 Wikipedia, Partition of a set EXAMPLE 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). MAPLE 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); MATHEMATICA 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]; Table[a[n], {n, 0, 45}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *) CROSSREFS Column k=9 of A274835. Sequence in context: A061511 A138142 A085890 * A134817 A067581 A099469 Adjacent sequences:  A274839 A274840 A274841 * A274843 A274844 A274845 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 08 2016 STATUS approved

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Last modified May 16 02:41 EDT 2021. Contains 343937 sequences. (Running on oeis4.)