A196234 Number of different ways to select 7 disjoint subsets from {1..n} with equal element sum.

1, 3, 12, 33, 114, 403, 1618, 8946, 45917, 189428, 979841, 5497818, 31708309, 178006222, 1091681487, 6207647636, 32636979255, 184162388392, 1069147827024, 6446977283374

Offset

13,2

Links

Table of n, a(n) for n=13..32.

Example

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

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, 7];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 13, 25}] (* Jean-François Alcover, Jun 08 2018, after Alois P. Heinz *)

Crossrefs

Column k=7 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196233, A196235, A196236, A196237.

Sequence in context: A159228 A054610 A183468 * A117655 A081423 A184705

Adjacent sequences: A196231 A196232 A196233 * A196235 A196236 A196237

Keyword

nonn,more

Author

Alois P. Heinz, Sep 29 2011

Extensions

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

a(29)-a(32) from Bert Dobbelaere, Sep 02 2019

Status

approved