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A196236 Number of different ways to select 9 disjoint subsets from {1..n} with equal element sum. 7
1, 3, 14, 40, 156, 554, 2369, 11841, 60654, 498320, 2987689, 15177178, 96041346, 656938806, 4640699138, 31263742313, 221075005249 (list; graph; refs; listen; history; text; internal format)
OFFSET

17,2

LINKS

Table of n, a(n) for n=17..33.

EXAMPLE

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

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, 9];

Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 17, 25}] (* Jean-Fran├žois Alcover, Jun 08 2018, after Alois P. Heinz *)

CROSSREFS

Column k=9 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196233, A196234, A196235, A196237.

Sequence in context: A005701 A050297 A117662 * A213482 A296267 A104905

Adjacent sequences:  A196233 A196234 A196235 * A196237 A196238 A196239

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Sep 29 2011

EXTENSIONS

a(29) from Alois P. Heinz, Nov 05 2014

a(30)-a(33) from Bert Dobbelaere, Sep 02 2019

STATUS

approved

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Last modified September 27 19:23 EDT 2021. Contains 347694 sequences. (Running on oeis4.)