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Search: id:A112972
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| A112972 |
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Number of ways the set {1,2,...,n} can be split into three subsets of equal sums. |
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+0
4
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| 0, 0, 0, 0, 1, 1, 0, 3, 9, 0, 43, 102, 0, 595, 1480, 0, 9294, 23728, 0, 157991, 411474, 0, 2849968, 7562583, 0, 53987864, 145173095, 0, 1061533318, 2885383960, 0, 21515805520, 59003023409, 0, 447142442841, 1235311936936, 0, 9489835046489
(list; graph; listen)
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OFFSET
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1,8
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FORMULA
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a(n) is 1/6 of the coefficient of x^0*y^0 in product(x^(-2k)+x^k(y^k+y^(-k), k=1..n).
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EXAMPLE
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For n=8 we have 84/75/6321, 84/732/651 and 831/75/642 so a(8)=3.
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MAPLE
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A112972:=proc(n) local i, j, p, t; t:= NULL; for j to n do p:=1; for i to j do p:=p*(x^(-2*i)+x^(i)*(y^i+y^(-i))); od; t:=t, coeff(coeff(p, x, 0), y, 0)/6; od; t; end;
with (numtheory): b:= proc() option remember; local i, j, t; `if` (args[1]=0, `if` (nargs=2, 1, b(args[t] $t=2..nargs)), add (`if` (args[j] -args[nargs] <0, 0, b(sort ([seq (args[i] -`if` (i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local m; m:= n*(n+1)/2; `if` (irem (m, 3)=0, b((m/3)$3, n)/6 , 0) end: seq (a(n), n=1..42); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2009]
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CROSSREFS
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Cf. A112956, A058377.
Sequence in context: A087566 A011337 A021723 this_sequence A016673 A103556 A010631
Adjacent sequences: A112969 A112970 A112971 this_sequence A112973 A112974 A112975
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KEYWORD
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nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 07 2005
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EXTENSIONS
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Extended beyond a(25) by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2009
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