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 A203017 Number of partitions of {1,2,...,3n} into 3 n-element subsets having the same sum. 2
 1, 0, 1, 2, 32, 305, 4331, 63261, 1025113, 17495345, 313692810, 5838204047, 112185853894, 2213711510395, 44691175805738, 920173212324164, 19274796589413439, 409908483736507979, 8835309887111026335, 192739853119591626715, 4250191938786946069812, 94641409538083474973850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The element sum of each subset is n*(3*n+1)/2 = A005449(n). LINKS Table of n, a(n) for n=0..21. Wikipedia, Partition of a set EXAMPLE a(0) = 1: {}, {}, {}. a(1) = 0: there is no partition of {1,2,3} into 3 1-element subsets having the same sum. a(2) = 1: {1,6}, {2,5}, {3,4}. a(3) = 2: {1,5,9}, {2,6,7}, {3,4,8}; {1,6,8}, {2,4,9}, {3,5,7}. MAPLE b:= proc() option remember; local i, j, t, k, m; m:= args[nargs-1]; k:= args[nargs-0]; if args[1]=0 then `if`(nargs=3, 1, b(args[t]\$t=2..nargs)) elif args[1]<1 then 0 else add(`if`(args[j] b((n*(3*n+1)/2 +n/97)\$3, 3*n, n)/`if`(n>0, 6, 1): seq(a(n), n=0..10); MATHEMATICA b[args_] := b[args] = Module[{nargs = Length[args], k = args[[-1]], m = args[[-2]]}, Which[args[[1]] == 0, If[nargs == 3, 1, b[args[[2 ;; nargs]] ]], args[[1]]<1, 0, True, Sum[If[args[[j]] < m, 0, b[Join[Sort[Table[ args[[i]] - If[i == j, m + 1/97, 0], {i, 1, nargs - 2}]], {m - 1, k}]]], {j, 1, nargs-2}]]]; A[n_, k_] := If[n == 0 || k == 0, 1, b[Join[Array[(k*(n*k + 1)/2 + k/97)&, n], {k*n, k}]]/n!]; a[k_] := A[3, k]; a /@ Range[0, 10] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *) CROSSREFS Row n=3 of A203986. Cf. A005449, A203435. Sequence in context: A158040 A202746 A212797 * A079766 A224293 A053065 Adjacent sequences: A203014 A203015 A203016 * A203018 A203019 A203020 KEYWORD nonn AUTHOR Alois P. Heinz, Jan 06 2012 STATUS approved

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Last modified August 13 01:27 EDT 2024. Contains 375113 sequences. (Running on oeis4.)