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

4,3

Links

Alois P. Heinz, Table of n, a(n) for n = 4..584

Wikipedia, Partition of a set

Formula

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

Crossrefs

Column k=4 of A287215.

Cf. A287253, A287254.

Sequence in context: A022639 A000589 A211830 * A226708 A206529 A118936

Adjacent sequences: A322874 A322875 A322876 * A322878 A322879 A322880

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved