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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. 2

%I #10 May 05 2020 04:28:28

%S 0,1,7,39,209,1123,6153,34723,202852,1229672,7742792,50653678,

%T 344195782,2427812876,17761759538,134650690097,1056676856777,

%U 8574943334545,71881479393513,621792661601615,5544644720281979,50918125911279963,481093310682127190

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

%H Alois P. Heinz, <a href="/A322876/b322876.txt">Table of n, a(n) for n = 3..586</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F a(n) = A287253(n) - A287252(n).

%p b:= proc(n, k, m, l) option remember; `if`(n<1, 1,

%p `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))

%p end:

%p A:= (n, k)-> b(n-1, min(k, n-1), 1, n):

%p a:= n-> (k-> A(n, k)-A(n, k-1))(3):

%p seq(a(n), n=3..30);

%t 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 A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];

%t a[n_] := With[{k = 3}, A[n, k] - A[n, k - 1]];

%t a /@ Range[3, 30] (* _Jean-François Alcover_, May 05 2020, after Maple *)

%Y Column k=3 of A287215.

%Y Cf. A287252, A287253.

%K nonn

%O 3,3

%A _Alois P. Heinz_, Dec 29 2018

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)