cp's OEIS Frontend

A196233 Number of different ways to select 6 disjoint subsets from {1..n} with equal element sum.

%I A196233 #19 Sep 05 2019 02:29:52
%S A196233 1,3,11,30,113,330,1284,5342,23976,141836,604359,2977297,15970382,
%T A196233 80990028,384959038,1943894348,10652582085,53759893907,292581087499,
%U A196233 1608101020113,8896321349456,51394417812545
%N A196233 Number of different ways to select 6 disjoint subsets from {1..n} with equal element sum.
%e A196233 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.
%t A196233 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 A196233 T[n_, k_] := Sum[b[Array[t&, k], n, k], {t, 2*k - 1, Floor[n*(n + 1)/(2*k) ]}]/k!;
%t A196233 a[n_] := T[n, 6];
%t A196233 Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 11, 25}] (* _Jean-François Alcover_, Jun 08 2018, after _Alois P. Heinz_ *)
%Y A196233 Column k=6 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196234, A196235, A196236, A196237.
%K A196233 nonn,more
%O A196233 11,2
%A A196233 _Alois P. Heinz_, Sep 29 2011
%E A196233 a(26) from _Alois P. Heinz_, Sep 25 2014
%E A196233 a(27)-a(32) from _Bert Dobbelaere_, Sep 05 2019