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Search: id:A113039
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| A113039 |
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Number of ways the set {1,2,...,n} can be split into three subsets of which the three sums are consecutive. |
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+0
1
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| 0, 0, 1, 0, 3, 5, 0, 23, 52, 0, 254, 593, 0, 3611, 8859, 0, 55554, 142169, 0, 946871, 2466282, 0, 17095813, 45359632, 0, 323760077, 870624976, 0, 6367406592, 17307580710, 0, 129063054631, 353941332518, 0, 2682355470491, 7410591325928
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The empty subset is not allowed, otherwise we would get a(2)=1. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2009]
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FORMULA
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a(n) is the coefficient of x^3y in product(x^(-2k)+x^k(y^k+y^(-k)), k=1..n) for n>2.
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EXAMPLE
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For n=5 we have splittings 4/23/15, 4/5/123, 13/5/24, so a(5)=3.
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MAPLE
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A113039:=proc(n) local i, j, p, t; t:= 0, 0; for j from 3 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, 3), y, 1); 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` (n>2 and irem (m, 3)=0, b(m/3-1, m/3, m/3+1, n), 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. A112972.
Sequence in context: A099895 A124222 A111823 this_sequence A093016 A031018 A146525
Adjacent sequences: A113036 A113037 A113038 this_sequence A113040 A113041 A113042
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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 12 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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