A196237 Number of different ways to select 10 disjoint subsets from {1..n} with equal element sum.

1, 3, 15, 44, 179, 741, 2989, 13932, 79433, 456134, 3096812, 21083037, 151022325, 1119202826, 8627014654

Offset

19,2

Links

Table of n, a(n) for n=19..33.

Example

a(20) = 3: {1,18}, {2,17}, {3,16}, {4,15}, {5,14}, {6,13}, {7,12}, {8,11}, {9,10}, {19} have element sum 19; {1,19}, {2,18}, {3,17}, {4,16}, {5,15}, {6,14}, {7,13}, {8,12}, {9,11}, {20} have element sum 20; {1,20}, {2,19}, {3,18}, {4,17}, {5,16}, {6,15}, {7,14}, {8,13}, {9,12}, {10,11} have element sum 21.

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, 10];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 19, 30}] (* Jean-François Alcover, Jun 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=10 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196233, A196234, A196235, A196236.

Sequence in context: A330322 A101165 A127407 * A177146 A161400 A112810

Adjacent sequences: A196234 A196235 A196236 * A196238 A196239 A196240

Keyword

nonn,more

Author

Alois P. Heinz, Sep 29 2011

Extensions

a(31)-a(33) from Bert Dobbelaere, Sep 02 2019

Status

approved