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A164934 Number of different ways to select 3 disjoint subsets from {1..n} with equal element sum. 11
0, 0, 0, 0, 1, 3, 8, 22, 63, 157, 502, 1562, 4688, 15533, 50953, 165054, 562376, 1911007, 6467143, 22447463, 78021923, 271410289, 957082911, 3384587525, 11998851674, 42876440587, 153684701645, 552421854011, 1995875594696, 7231871165277, 26274832876337 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

a(5) = 1, because {1,4}, {2,3}, {5} are disjoint subsets of {1..5} with element sum 5.

a(6) = 3: {1,4}, {2,3}, {5} have element sum 5, {1,5}, {2,4}, {6} have element sum 6, and {1,6}, {2,5}, {3,4} have element sum 7.

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 1..104 (first 65 terms from Alois P. Heinz)

FORMULA

Conjecture: a(n) ~ 4^n / (Pi * sqrt(3) * n^3). - Vaclav Kotesovec, Oct 16 2014

MAPLE

b:= proc(n, k, i) option remember; local m;

      m:= i*(i+1)/2;

      if k>n then b(k, n, i)

    elif k>=0 and n+k>m or k<0 and n-2*k>m then 0

    elif [n, k, i] = [0, 0, 0] then 1

    else b(n, k, i-1)+b(n+i, k+i, i-1)+b(n-i, k, i-1)+b(n, k-i, i-1)

      fi

    end:

a:= proc(n) option remember;

      `if`(n>2, b(n, n, n-1)/2+ a(n-1), 0)

    end:

seq(a(n), n=1..20);

MATHEMATICA

b[n_, k_, i_] := b[n, k, i] = Module[{m = i*(i+1)/2}, Which[k>n , b[k, n, i], k >= 0 && n+k>m || k<0 && n-2*k > m, 0, {n, k, i} == {0, 0, 0}, 1, True, b[n, k, i-1] + b[n+i, k+i, i-1] + b[n-i, k, i-1] + b[n, k-i, i-1]]]; a[n_] := a[n] = If[n>2, b[n, n, n-1]/2 + a[n-1], 0]; Table[a[n], {n, 1, 20}] (* Jean-Fran├žois Alcover, Feb 05 2015, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A196231.

Cf. A161943, A164949, A232534.

Sequence in context: A188464 A298260 A317997 * A047926 A192681 A014138

Adjacent sequences:  A164931 A164932 A164933 * A164935 A164936 A164937

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 2009

STATUS

approved

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Last modified October 18 18:10 EDT 2018. Contains 316323 sequences. (Running on oeis4.)