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A322876 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals three.

%I A322876 #10 May 05 2020 04:28:28
%S A322876 0,1,7,39,209,1123,6153,34723,202852,1229672,7742792,50653678,
%T A322876 344195782,2427812876,17761759538,134650690097,1056676856777,
%U A322876 8574943334545,71881479393513,621792661601615,5544644720281979,50918125911279963,481093310682127190
%N A322876 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals three.
%H A322876 Alois P. Heinz, <a href="/A322876/b322876.txt">Table of n, a(n) for n = 3..586</a>
%H A322876 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322876 a(n) = A287253(n) - A287252(n).
%p A322876 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322876      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322876     end:
%p A322876 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322876 a:= n-> (k-> A(n, k)-A(n, k-1))(3):
%p A322876 seq(a(n), n=3..30);
%t A322876 b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m b[n - 1, k, m, l]];
%t A322876 A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
%t A322876 a[n_] := With[{k = 3}, A[n, k] - A[n, k - 1]];
%t A322876 a /@ Range[3, 30] (* _Jean-François Alcover_, May 05 2020, after Maple *)
%Y A322876 Column k=3 of A287215.
%Y A322876 Cf. A287252, A287253.
%K A322876 nonn
%O A322876 3,3
%A A322876 _Alois P. Heinz_, Dec 29 2018