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Search: id:A078478
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| A078478 |
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Number of rational knots of n crossings with signature 0 (chiral pairs counted twice). |
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+0
4
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| 0, 1, 0, 3, 2, 9, 6, 29, 30, 99, 112, 351, 450, 1275, 1734, 4707, 6762, 17577, 26208, 66197, 101862, 250953, 395804, 956385, 1540110, 3660541, 5997600, 14061141, 23382294, 54177741, 91246662, 209295261, 356432166, 810375651, 1393592512
(list; graph; listen)
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OFFSET
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3,4
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LINKS
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A. Stoimenow, Generating Functions, Fibonacci Numbers and Rational Knots
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FORMULA
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Generating function = (-x/2)*( 2 + (2*x^4-x^2-1)/(sqrt(1-4*x^4)*(1+x^2)) + (2*x^2-x-1)/(sqrt(1-4*x^2)*(1+x)) ) - Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 01 2006
a(2n+4) = A006134(n-1) = Sum[ (2k)!/(k!)^2, {k,0,n} ]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 23 2007
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CROSSREFS
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Cf. A006134.
Sequence in context: A164279 A125152 A082819 this_sequence A019778 A134480 A011323
Adjacent sequences: A078475 A078476 A078477 this_sequence A078479 A078480 A078481
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 03 2003
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 01 2006
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