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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
0, 1, 7, 39, 209, 1123, 6153, 34723, 202852, 1229672, 7742792, 50653678, 344195782, 2427812876, 17761759538, 134650690097, 1056676856777, 8574943334545, 71881479393513, 621792661601615, 5544644720281979, 50918125911279963, 481093310682127190 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)