A196232 Number of different ways to select 5 disjoint subsets from {1..n} with equal element sum.

1, 3, 10, 26, 83, 322, 1182, 3971, 15662, 69371, 328016, 1460297, 6080910, 26901643, 123926071, 598722099, 2838432721, 13220493552, 63710261040, 312134646974, 1554373859464, 7673048166979, 37597940705361, 186986406578372

Offset

9,2

Links

Table of n, a(n) for n=9..32.

Example

a(10) = 3: {1,8}, {2,7}, {3,6}, {4,5}, {9} have element sum 9; {1,9}, {2,8}, {3,7}, {4,6}, {10} have element sum 10; {1,10}, {2,9}, {3,8}, {4,7}, {5,6} have element sum 11.

Mathematica

b[l_, n_, k_] := b[l, n, k] = Module[{i, j}, 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}] ]];
T[n_, k_] := Sum[b[Array[t &, k], n, k], {t, 2*k - 1, Floor[n*(n + 1)/(2*k) ]}]/k!;
a[n_] := T[n, 5];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 9, 25}] (* Jean-François Alcover, Jun 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=5 of A196231. Cf. A000225, A161943, A164934, A164949, A196233, A196234, A196235, A196236, A196237.

Sequence in context: A269965 A110158 A301308 * A282282 A105660 A056681

Adjacent sequences: A196229 A196230 A196231 * A196233 A196234 A196235

Keyword

nonn,more

Author

Alois P. Heinz, Sep 29 2011

Extensions

a(26)-a(28) from Alois P. Heinz, Sep 25 2014

a(29)-a(32) from Bert Dobbelaere, Sep 05 2019

Status

approved