A196233 Number of different ways to select 6 disjoint subsets from {1..n} with equal element sum.

1, 3, 11, 30, 113, 330, 1284, 5342, 23976, 141836, 604359, 2977297, 15970382, 80990028, 384959038, 1943894348, 10652582085, 53759893907, 292581087499, 1608101020113, 8896321349456, 51394417812545

Offset: 11

Author

Alois P. Heinz, Sep 29 2011

Keywords

• nonn
• more

Examples

			a(12) = 3: {1,10}, {2,9}, {3,8}, {4,7}, {5,6}, {11} have element sum 11; {1,11}, {2,10}, {3,9}, {4,8}, {5,7}, {12} have element sum 12; {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, {6,7} have element sum 13.
		

Crossrefs

Column k=6 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, 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, 6];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 11, 25}] (* Jean-François Alcover, Jun 08 2018, after Alois P. Heinz *)

Extensions

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

a(27)-a(32) from Bert Dobbelaere, Sep 05 2019