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

0, 1, 7, 39, 209, 1123, 6153, 34723, 202852, 1229672, 7742792, 50653678, 344195782, 2427812876, 17761759538, 134650690097, 1056676856777, 8574943334545, 71881479393513, 621792661601615, 5544644720281979, 50918125911279963, 481093310682127190

Offset

3,3

Links

Alois P. Heinz, Table of n, a(n) for n = 3..586

Wikipedia, Partition of a set

Formula

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

Maple

b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
     `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
    end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(3):
seq(a(n), n=3..30);

Mathematica

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]];
A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
a[n_] := With[{k = 3}, A[n, k] - A[n, k - 1]];
a /@ Range[3, 30] (* Jean-François Alcover, May 05 2020, after Maple *)

Crossrefs

Column k=3 of A287215.

Cf. A287252, A287253.

Sequence in context: A016127 A099460 A246987 * A092923 A164550 A125786

Adjacent sequences: A322873 A322874 A322875 * A322877 A322878 A322879

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved