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Search: id:A060005
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| A060005 |
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Number of ways of partitioning the integers {1,2,..,4n} into two (unordered) sets such that the sums of parts are equal in both sets (parts in either set will add up to (4n)*(4n+1)/4). Number of solutions to {1 +- 2 +- 3 +- ... +- 4n=0}. |
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7
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| 1, 1, 7, 62, 657, 7636, 93846, 1199892, 15796439, 212681976, 2915017360, 40536016030, 570497115729, 8110661588734, 116307527411482, 1680341334827514, 24435006625667338, 357366669614512168
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991), 315-324.
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LINKS
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S. R. Finch, Signum equations and extremal coefficients.
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FORMULA
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a(0)=1 and a(n) is half the coefficient of q^0 in product('(q^(-k)+q^k)', 'k'=1..4*n) for n >= 1.
n>=1, a(n)=(1/Pi)*16^n*J(4n) where J(n)=integral(t=0,Pi/2,cos(t)cos(2t)...cos(nt)dt) - Benoit Cloitre (abmt(AT)orange.fr), Sep 24 2006
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EXAMPLE
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a(1)=1 since there is only one way of partitioning {1,2,3,4} into two sets of equal sum, namely {1,4}, {2,3}.
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CROSSREFS
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Cf. A060468, A007219, A107350, a(n)=A058377(4n)
Sequence in context: A145507 A047685 A024089 this_sequence A055066 A167550 A161201
Adjacent sequences: A060002 A060003 A060004 this_sequence A060006 A060007 A060008
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KEYWORD
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nonn
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AUTHOR
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Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Mar 15 2001
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