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Search: id:A028723
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| A028723 |
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(1/4)*floor(n/2)*floor((n-1)/2)*floor((n-2)/2)*floor((n-3)/2). |
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+0
5
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| 0, 0, 0, 0, 0, 1, 3, 9, 18, 36, 60, 100, 150, 225, 315, 441, 588, 784, 1008, 1296, 1620, 2025, 2475, 3025, 3630, 4356, 5148, 6084, 7098, 8281, 9555, 11025, 12600, 14400, 16320, 18496, 20808, 23409, 26163, 29241
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Conjectured to be crossing number of complete graph K_n, see A000241.
Comment from Erich Friedman (erich.friedman(AT)stetson.edu): also the maximum number of rectangles that can be formed from n lines.
Number of symmetric Dyck paths of semilength n and having five peaks. E.g. a(6)=3 because we have U*DU*DUU*DDU*DU*D, U*DUU*DU*DU*DDU*D, and UU*DU*DU*DU*DU*DD, where U=(1,1), D=(1,-1) and * indicates a peak. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 12 2004
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REFERENCES
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Martin Gardner, Knotted Doughnuts, Chapter 11, pages 133-144.
C. Thomassen, Embeddings and Minors, in Handbook of Combinatorics, p. 314.
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LINKS
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J. Dolan et al., su(3) and Zarankiewicz's conjecture
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FORMULA
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If n even, n*(n-2)^2 *(n-4)/64; if n odd, (n-1)^2 *(n-3)^2/64.
G.f.=z^5*(1+z+z^2)/[(1-z)^5*(1+z)^3]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 12 2004
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MATHEMATICA
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Table[ If[ EvenQ[n], n(n - 2)^2(n - 4)/64, (n - 1)^2(n - 3)^2/64], {n, 0, 50} ]
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CROSSREFS
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It is not known if A000241 and A028723 agree. Cf. A006918.
Cf. A000241, A028723.
Sequence in context: A132920 A127645 A000241 this_sequence A057578 A015635 A062882
Adjacent sequences: A028720 A028721 A028722 this_sequence A028724 A028725 A028726
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KEYWORD
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nonn
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AUTHOR
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njas
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