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A060468
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Number of fair distributions (equal sum) of the integers {1,..,4n} between A and B = number of solutions to the equation {\pm 1\pm 2\pm3\dots\pm 4n=0}.
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4
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1, 2, 14, 124, 1314, 15272, 187692, 2399784, 31592878, 425363952, 5830034720, 81072032060, 1140994231458, 16221323177468, 232615054822964, 3360682669655028, 48870013251334676, 714733339229024336
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| S. R. Finch, Signum equations and extremal coefficients.
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FORMULA
| a(n) = coefficient of q^0 in product('(q^(-k)+q^k)', 'k' = 1..4*n).
a(n) = A025591(4n) = A063865(4n) = A063867(4n) = 2*A060005(n). Seems to be close to sqrt(3/32pi)*16^n/sqrt(n^3+n^2*0.6+n*0.1385...) and sqrt(n*pi/2)*A063074(n). - Henry Bottomley (se16(AT)btinternet.com), Jul 30 2005
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EXAMPLE
| a(1)=2: give either the set {1,4} to A and {2,3} to B or give {2,3} to A and {1,4} to B.
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CROSSREFS
| Sequence in context: A192457 A155728 A199560 * A121082 A155650 A168658
Adjacent sequences: A060465 A060466 A060467 * A060469 A060470 A060471
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KEYWORD
| nice,nonn
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AUTHOR
| Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Mar 15 2001
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