A196235 Number of different ways to select 8 disjoint subsets from {1..n} with equal element sum.

1, 3, 13, 37, 134, 466, 1916, 9409, 46006, 255714, 1525052, 9524779, 58944302, 355219704, 2315784192, 14568780212, 97993669291, 619342933593

Offset

15,2

Links

Table of n, a(n) for n=15..32.

Example

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

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, 8];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 15, 25}] (* Jean-François Alcover, Jun 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=8 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196233, A196234, A196236, A196237.

Sequence in context: A256316 A194486 A024535 * A120479 A146227 A019007

Adjacent sequences: A196232 A196233 A196234 * A196236 A196237 A196238

Keyword

nonn,more

Author

Alois P. Heinz, Sep 29 2011

Extensions

a(27)-a(28) from Alois P. Heinz, Nov 05 2014

a(29)-a(32) from Bert Dobbelaere, Sep 01 2019

Status

approved