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

11,2

Links

Table of n, a(n) for n=11..32.

Example

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.

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 *)

Crossrefs

Column k=6 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196234, A196235, A196236, A196237.

Sequence in context: A346848 A330148 A085376 * A009131 A003554 A003523

Adjacent sequences: A196230 A196231 A196232 * A196234 A196235 A196236

Keyword

nonn,more

Author

Alois P. Heinz, Sep 29 2011

Extensions

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

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

Status

approved