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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-François 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 January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)