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Search: id:A071801
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| A071801 |
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Binomial(2n, n)-binomial(n, floor(n/2))^2 |
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+0
3
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| 0, 1, 2, 11, 34, 152, 524, 2207, 7970, 32744, 121252, 491988, 1850380, 7455944, 28337976, 113708295, 435443490, 1742630120, 6711230900, 26811568916, 103711749284, 413849297784, 1606464657096, 6405315809516, 24935144010764
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of lattice paths in the lattice [0..n] X [0..n] which do not pass through the point (Floor(n/2),Floor(n/2)). In this case, the "hole" in the lattice is at the point closest to the lattice center.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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Also, a(n) = Sum_{m=0..n} binomial(n, m)^2 - binomial(n, floor(n/2))^2.
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MATHEMATICA
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Table[Binomial[2n, n]-Binomial[n, Floor[n/2]]^2, {n, 2, 20}]
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CROSSREFS
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a[n]=A000984[n]-A001405[n]^2
Cf. A000984, A001405, A002894, A071800, A071803.
Adjacent sequences: A071798 A071799 A071800 this_sequence A071802 A071803 A071804
Sequence in context: A100109 A026961 A026971 this_sequence A026981 A027223 A027229
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 06 2002
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EXTENSIONS
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More terms from Roger Bagula (rlbagulatftn(AT)yahoo.com), Aug 28 2006
Edited by njas, Oct 08 2006
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