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A322877 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals four.

%I A322877 #8 May 05 2020 04:28:33
%S A322877 0,1,11,77,493,3124,20019,130916,878249,6063134,43144661,316670184,
%T A322877 2397764986,18726889938,150814853887,1251834352246,10703915163764,
%U A322877 94227518620167,853463133257984,7948557602950239,76069254546156710,747596311576859585,7540213445348427312
%N A322877 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals four.
%H A322877 Alois P. Heinz, <a href="/A322877/b322877.txt">Table of n, a(n) for n = 4..584</a>
%H A322877 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322877 a(n) = A287254(n) - A287253(n).
%p A322877 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322877      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322877     end:
%p A322877 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322877 a:= n-> (k-> A(n, k)-A(n, k-1))(4):
%p A322877 seq(a(n), n=4..30);
%t A322877 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 A322877 A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
%t A322877 a[n_] := With[{k = 4}, A[n, k] - A[n, k - 1]];
%t A322877 a /@ Range[4, 30] (* _Jean-François Alcover_, May 05 2020, after Maple *)
%Y A322877 Column k=4 of A287215.
%Y A322877 Cf. A287253, A287254.
%K A322877 nonn
%O A322877 4,3
%A A322877 _Alois P. Heinz_, Dec 29 2018