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

0, 1, 11, 77, 493, 3124, 20019, 130916, 878249, 6063134, 43144661, 316670184, 2397764986, 18726889938, 150814853887, 1251834352246, 10703915163764, 94227518620167, 853463133257984, 7948557602950239, 76069254546156710, 747596311576859585, 7540213445348427312

Offset: 4

Author

Alois P. Heinz, Dec 29 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..584
• Wikipedia, Partition of a set

Crossrefs

Column k=4 of A287215.

Cf. A287253, A287254.

Programs

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))(4):
seq(a(n), n=4..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 = 4}, A[n, k] - A[n, k - 1]];
a /@ Range[4, 30] (* Jean-François Alcover, May 05 2020, after Maple *)

Formula

a(n) = A287254(n) - A287253(n).