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A113035
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Number of ways the set {1,2,...,n} can be split into two subsets of which the sum of one is twice the sum of the other.
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1
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0, 1, 1, 0, 3, 4, 0, 10, 17, 0, 46, 78, 0, 231, 401, 0, 1233, 2177, 0, 6869, 12268, 0, 39502, 71172, 0, 232686, 422076, 0, 1396669, 2547246, 0, 8512170, 15593760, 0, 52534875, 96598865, 0, 327669853, 604405633, 0, 2062171364, 3814087419, 0, 13078921499
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n) is the coefficient of x^0 in product(x^(-2k)+x^k, k=1..n).
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EXAMPLE
| For n=5 we have 5/1234,14/532 and 23/541 so a(5)=3.
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MAPLE
| A113035:= 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)); od; t:=t, coeff(p, x, 0); od; t; end;
##
b:= proc(n, i) option remember; local m;
m:= i*(i+1)/2;
`if` (n>m, 0, `if` (n=m, 1, b(abs(n-i), i-1) +b(n+i, i-1)))
end:
a:= n-> `if`(irem(n, 3)=1, 0, b(n*(n+1)/6, n)):
seq (a(n), n=1..60); # Alois P. Heinz, Oct 31 2011
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CROSSREFS
| Cf. A058377, A112972.
Sequence in context: A049251 A158674 A056862 * A099447 A078067 A192442
Adjacent sequences: A113032 A113033 A113034 * A113036 A113037 A113038
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KEYWORD
| nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com),Oct 11 2005
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