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

Author

Alois P. Heinz, Sep 29 2011

Keywords

• nonn
• more

Examples

			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.
		

Crossrefs

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

Programs

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 *)

Extensions

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

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