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 A164949 Number of different ways to select 4 disjoint subsets from {1..n} with equal element sum. 9
 0, 0, 0, 0, 0, 0, 1, 3, 9, 23, 67, 203, 693, 2584, 9929, 37480, 137067, 522854, 2052657, 8199728, 33456333, 137831268, 574295984, 2392149818, 9950364020, 41860671346, 177512155194, 757447761138, 3254519322231, 14049972380612, 60960849334377, 265354255338637 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS EXAMPLE a(7) = 1, because {1,6}, {2,5}, {3,4}, {7} are disjoint subsets of {1..7} with element sum 7. a(8) = 3: {1,6}, {2,5}, {3,4}, {7} have element sum 7, {1,7}, {2,6}, {3,5}, {8} have element sum 8, and {1,8}, {2,7}, {3,6}, {4,5} have element sum 9. MAPLE b:= proc() option remember; local i, j; `if`(args[1]=0 and args[2]=0 and args[3]=0 and args[4]=0, 1, `if`(add(args[j], j=1..4)> args[5] *(args[5]-1)/2, 0, b(args[j]\$j=1..4, args[5]-1)) +add(`if`(args[j] -args[5]<0, 0, b(sort([seq(args[i] -`if`(i=j, args[5], 0), i=1..4)])[], args[5]-1)), j=1..4)) end: a:= n-> add(b(k\$4, n), k=7..floor(n*(n+1)/8)) /24: seq(a(n), n=1..20); 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, 2k-1, Floor[n(n+1)/(2k)]}]/k!; a[n_] := T[n, 4]; Array[a, 20] (* Jean-François Alcover, Jun 08 2018, after Alois P. Heinz's Maple code in A196231 *) CROSSREFS Column k=4 of A196231. Cf. A161943, A164934. Sequence in context: A253244 A018044 A047045 * A146661 A004666 A196488 Adjacent sequences:  A164946 A164947 A164948 * A164950 A164951 A164952 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 01 2009 STATUS approved

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Last modified October 14 11:59 EDT 2019. Contains 328001 sequences. (Running on oeis4.)