|
%I #16 Sep 02 2019 14:39:09
%S 1,3,15,44,179,741,2989,13932,79433,456134,3096812,21083037,151022325,
%T 1119202826,8627014654
%N Number of different ways to select 10 disjoint subsets from {1..n} with equal element sum.
%e 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.
%t 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 T[n_, k_] := Sum[b[Array[t &, k], n, k], {t, 2*k - 1, Floor[n*(n + 1)/(2*k) ]}]/k!;
%t a[n_] := T[n, 10];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 19, 30}] (* _Jean-François Alcover_, Jun 08 2018, after _Alois P. Heinz_ *)
%Y Column k=10 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196233, A196234, A196235, A196236.
%K nonn,more
%O 19,2
%A _Alois P. Heinz_, Sep 29 2011
%E a(31)-a(33) from _Bert Dobbelaere_, Sep 02 2019
|
