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A287252 Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks are <= two.

%I A287252 #14 May 28 2018 03:25:50
%S A287252 1,1,2,5,14,44,152,571,2317,10096,47013,232944,1223428,6786936,
%T A287252 39640947,243060305,1560340480,10461611439,73094563140,531127372268,
%U A287252 4006242743228,31316162403165,253292622192153,2116823651781702,18255325000268015,162261535224570326
%N A287252 Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks are <= two.
%H A287252 Alois P. Heinz, <a href="/A287252/b287252.txt">Table of n, a(n) for n = 0..590</a>
%H A287252 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A287252 a(n) = A287216(n,2).
%F A287252 a(n) = A000110(n) for n <= 3.
%p A287252 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A287252      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A287252     end:
%p A287252 a:= n-> b(n-1, min(2, n-1), 1, n):
%p A287252 seq(a(n), n=0..30);
%t A287252 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 A287252 a[n_] := b[n - 1, Min[2, n - 1], 1, n];
%t A287252 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 28 2018, from Maple *)
%Y A287252 Column k=2 of A287216.
%Y A287252 Cf. A000110.
%K A287252 nonn
%O A287252 0,3
%A A287252 _Alois P. Heinz_, May 22 2017