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A274838 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of five.

%I A274838 #10 May 15 2018 08:34:36
%S A274838 1,1,1,1,1,1,2,3,4,5,6,13,26,49,88,151,397,951,2145,4633,9643,28898,
%T A274838 80843,214126,542081,1317924,4392295,13871122,41984457,122463762,
%U A274838 344409561,1273659431,4463980333,14994032599,48610148069,152506484015,614168698264
%N A274838 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of five.
%H A274838 Alois P. Heinz, <a href="/A274838/b274838.txt">Table of n, a(n) for n = 0..808</a>
%H A274838 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A274838 a(7) = 3: 16|27|3|4|5, 1|27|3|4|5|6, 1|2|3|4|5|6|7.
%e A274838 a(8) = 4: 16|27|38|4|5, 1|27|38|4|5|6, 1|2|38|4|5|6|7, 1|2|3|4|5|6|7|8.
%e A274838 a(9) = 5: 16|27|38|49|5, 1|27|38|49|5|6, 1|2|38|49|5|6|7, 1|2|3|49|5|6|7|8, 1|2|3|4|5|6|7|8|9.
%p A274838 b:= proc(n, m, t) option remember; `if`(n=0, 1,
%p A274838      add(`if`(irem(j-t, 5)=0, b(n-1, max(m, j),
%p A274838               irem(t+1, 5)), 0), j=1..m+1))
%p A274838     end:
%p A274838 a:= n-> b(n, 0, 1):
%p A274838 seq(a(n), n=0..40);
%t A274838 b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 5] == 0, b[n - 1, Max[m, j], Mod[t + 1, 5]], 0], {j, 1, m + 1}]];
%t A274838 a[n_] := b[n, 0, 1];
%t A274838 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A274838 Column k=5 of A274835.
%K A274838 nonn
%O A274838 0,7
%A A274838 _Alois P. Heinz_, Jul 08 2016