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A274841 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of eight.

%I A274841 #9 May 15 2018 08:34:59
%S A274841 1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,19,38,73,136,247,438,757,1268,3303,
%T A274841 7883,17801,38745,82179,170907,349341,700517,2066512,5768089,15386070,
%U A274841 39563059,98692628,239843745,569063602,1318211431,4290275275,13443268926
%N A274841 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of eight.
%H A274841 Alois P. Heinz, <a href="/A274841/b274841.txt">Table of n, a(n) for n = 0..902</a>
%H A274841 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A274841 a(8) = 1: 1|2|3|4|5|6|7|8.
%e A274841 a(9) = 2: 19|2|3|4|5|6|7|8, 1|2|3|4|5|6|7|8|9.
%e A274841 a(10) = 3: 19|2(10)|3|4|5|6|7|8, 1|2(10)|3|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).
%p A274841 b:= proc(n, m, t) option remember; `if`(n=0, 1,
%p A274841      add(`if`(irem(j-t, 8)=0, b(n-1, max(m, j),
%p A274841               irem(t+1, 8)), 0), j=1..m+1))
%p A274841     end:
%p A274841 a:= n-> b(n, 0, 1):
%p A274841 seq(a(n), n=0..45);
%t A274841 b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 8] == 0, b[n - 1, Max[m, j], Mod[t + 1, 8]], 0], {j, 1, m + 1}]];
%t A274841 a[n_] := b[n, 0, 1];
%t A274841 Table[a[n], {n, 0, 45}] (* _Jean-François Alcover_, May 15 2018, after _Alois P. Heinz_ *)
%Y A274841 Column k=8 of A274835.
%K A274841 nonn
%O A274841 0,10
%A A274841 _Alois P. Heinz_, Jul 08 2016