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Search: id:A113038
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| A113038 |
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Number of ways the set {1,2,...,n} can be split into three subsets of which the sum of one is one more than the equal sums of both other subsets. |
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+0
1
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| 0, 0, 0, 1, 0, 0, 5, 0, 0, 60, 0, 0, 747, 0, 0, 11076, 0, 0, 183092, 0, 0, 3238140, 0, 0, 60475317, 0, 0, 1175471401, 0, 0, 23600724220, 0, 0, 486653058995, 0, 0, 10260353188386, 0, 0, 220439819437387, 0, 0, 4813287355239594, 0, 0
(list; graph; listen)
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OFFSET
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1,7
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FORMULA
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a(n) is half the coefficient of xy in product(x^(-2k)+x^k(y^k+y^(-k)), k=1..n) for n>1.
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EXAMPLE
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For n=7 we have splittings 36/27/145, 36/127/45, 136/27/45,
135/27/46, 126/45/37 so a(7)=5.
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MAPLE
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A113038:=proc(n) local i, j, p, t; t:= 0; for j from 2 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, 1), y, 1)/2; 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` (m>3 and irem (m, 3)=1, b((m-1)/3, (m-1)/3, (m-1)/3+1, n)/2, 0) end: seq (a(n), n=1..50); [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: A019178 A075534 A083527 this_sequence A082512 A068385 A071086
Adjacent sequences: A113035 A113036 A113037 this_sequence A113039 A113040 A113041
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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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