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A274843 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of ten.

%I A274843 #9 May 15 2018 08:35:11
%S A274843 1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,11,23,46,89,168,311,566,
%T A274843 1013,1780,3059,5106,13283,31683,71545,155833,331139,691387,1424525,
%U A274843 2902605,5848135,11610871,34108236,95170569,254432006,657159051,1650540916
%N A274843 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of ten.
%H A274843 Alois P. Heinz, <a href="/A274843/b274843.txt">Table of n, a(n) for n = 0..953</a>
%H A274843 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A274843 a(10) = 1: 1|2|3|4|5|6|7|8|9|(10).
%e A274843 a(11) = 2: 1(11)|2|3|4|5|6|7|8|9|(10), 1|2|3|4|5|6|7|8|9|(10)|(11).
%p A274843 b:= proc(n, m, t) option remember; `if`(n=0, 1,
%p A274843      add(`if`(irem(j-t, 10)=0, b(n-1, max(m, j),
%p A274843               irem(t+1, 10)), 0), j=1..m+1))
%p A274843     end:
%p A274843 a:= n-> b(n, 0, 1):
%p A274843 seq(a(n), n=0..50);
%t A274843 b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 10] == 0, b[n - 1, Max[m, j], Mod[t + 1, 10]], 0], {j, 1, m + 1}]];
%t A274843 a[n_] := b[n, 0, 1];
%t A274843 Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A274843 Column k=10 of A274835.
%K A274843 nonn
%O A274843 0,12
%A A274843 _Alois P. Heinz_, Jul 08 2016