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%I #9 May 15 2018 08:35:05
%S 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,
%T 2547,6629,15815,35713,77769,165155,344379,707693,1434461,2859871,
%U 8415994,23485835,62727630,161710529,404995340,989816263,2367377650,5547588797
%N Number of set partitions of [n] such that the difference between each element and its block index is a multiple of nine.
%H Alois P. Heinz, <a href="/A274842/b274842.txt">Table of n, a(n) for n = 0..928</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e a(9) = 1: 1|2|3|4|5|6|7|8|9.
%e a(10) = 2: 1(10)|2|3|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).
%e 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).
%p b:= proc(n, m, t) option remember; `if`(n=0, 1,
%p add(`if`(irem(j-t, 9)=0, b(n-1, max(m, j),
%p irem(t+1, 9)), 0), j=1..m+1))
%p end:
%p a:= n-> b(n, 0, 1):
%p seq(a(n), n=0..45);
%t 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}]];
%t a[n_] := b[n, 0, 1];
%t Table[a[n], {n, 0, 45}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y Column k=9 of A274835.
%K nonn
%O 0,11
%A _Alois P. Heinz_, Jul 08 2016
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