A322875 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals two.

0, 1, 5, 21, 86, 361, 1584, 7315, 35635, 183080, 990659, 5635021, 33622161, 209973099, 1369560267, 9310957518, 65852852210, 483672626464, 3683088047043, 29033382412670, 236591717703447, 1990467019391404, 17268021545339042, 154304401318961489

Offset

2,3

Links

Alois P. Heinz, Table of n, a(n) for n = 2..590

Wikipedia, Partition of a set

Formula

a(n) = A287252(n) - A026898(n-1).

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))(2):
seq(a(n), n=2..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 = 2}, A[n, k] - A[n, k - 1]];
a /@ Range[2, 30] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A287215.

Cf. A026898, A287252.

Sequence in context: A265939 A012814 A039919 * A292494 A010925 A019992

Adjacent sequences: A322872 A322873 A322874 * A322876 A322877 A322878

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved