cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A196534 Number of different ways to select disjoint nonempty subsets from {1..n} with equal element sum.

Original entry on oeis.org

1, 3, 8, 18, 39, 83, 179, 388, 857, 1914, 4494, 10844, 26923, 70645, 192297, 538646, 1579602, 4793718, 15010425, 48941642, 164010913, 566065123, 2025354291, 7450901462, 27986863322, 107940691328
Offset: 1

Views

Author

Alois P. Heinz, Oct 03 2011

Keywords

Comments

A000225(n) <= a(n) <= A058692(n+1).

Examples

			a(3) = 8: {{1}}, {{2}}, {{3}}, {{1,2}}, {{1,3}}, {{2,3}}, {{1,2,3}}, {{1,2},{3}}. Element sums are 1, 2, 3, 3, 4, 5, 6, and 3, respectively.
		

Crossrefs

Programs

  • Maple
    b:= proc(l, n, k) option remember; local i, j; `if`(l=[0$k], 1, `if`(add(j, j=l)>n*(n-1)/2, 0, b(l, n-1, k))+ add(`if`(l[j]-n<0, 0, b(sort([seq(l[i] -`if`(i=j, n, 0), i=1..k)]), n-1, k)), j=1..k)) end: a:= n-> add(add(b([t$k], n, k), t=2*k-1..floor(n*(n+1)/(2*k)))/k!, k=1..n): seq(a(n), n=1..15);
  • Mathematica
    b[l_, n_, k_] := b[l, n, k] = If[l == Array[0&, k], 1, If[Total[l] > n*(n-1)/2, 0, b[l, n-1, k]] + Sum[If[l[[j]]-n < 0, 0, b[Sort[Table[ l[[i]] - If[i == j, n, 0], {i, 1, k}]], n-1, k]], {j, 1, k}]];
    a[n_] := Sum[Sum[b[Array[t&, k], n, k], {t, 2*k-1, Floor[n*(n+1)/(2*k)]} ]/k!, {k, 1, Ceiling[n/2]}];
    Table[Print[n, " ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Jun 01 2022, after Alois P. Heinz *)

Extensions

a(26) from Alois P. Heinz, Oct 20 2014