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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
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.
Sequence in context: A298260 A336990 A317997 * A047926 A192681 A339288
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2009
STATUS
approved