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A261497
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Number of necklaces with n white beads and 3*n black beads.
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3
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1, 1, 4, 19, 116, 776, 5620, 42288, 328756, 2615104, 21191904, 174303163, 1451430692, 12211799224, 103655949072, 886568153744, 7633233556276, 66105170315084, 575445692499952, 5032380942945322, 44191451788248416, 389514699013012242, 3444925385336301684
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, Necklace
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FORMULA
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a(n) = 1/(4*n) * Sum_{d|n} C(4*n/d,n/d) * A000010(d) for n>0, a(0) = 1.
a(n) ~ 2^(8*n-3/2) / (3^(3*n) * sqrt(3*Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015
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MAPLE
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with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(4*n/d, n/d)
*phi(d), d=divisors(n))/(4*n)):
seq(a(n), n=0..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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