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Search: id:A090596
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| A090596 |
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a(n) = - a(n-1) + 5[a(n-2)+a(n-3)] - 2[a(n-4)+a(n-5)] - 8[a(n-6)+a(n-7)] |
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+0
3
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| 1, 1, 2, 3, 7, 12, 24, 45, 91, 176, 352, 693, 1387, 2752, 5504, 10965, 21931, 43776, 87552, 174933, 349867, 699392, 1398784, 2796885, 5593771, 11186176, 22372352, 44741973, 89483947, 178962432
(list; graph; listen)
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OFFSET
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3,3
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COMMENT
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Conjectured to coincide with the sequence of rational knots with n crossings, A018240.
Conjecture derived from: s(n) = k(n) + l(n): definition of sum of rational knots (k) and links (l) s(n) = 6s(n-2) -8s(n-4): see A005418 (Jablan's observation) d(n) = d(n-2) + 2d(n-4): see A001045 (modified Jacobsthal sequence) l(n) = k(n-1) + d(n): conjecture
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REFERENCES
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Jablan S. and Sazdanovic R., LinKnot: Knot Theory by Computer, World Scientific Press, 2007.
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FORMULA
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a(n) = {2^{n-3}+2^{[n/2]-2^{n (mod 2)}+ {[n/2] (mod 2)}(-1)^{n-1}}/3. - Slavik Jablan, Dec 20 2003
G.f.: (1-2x^2-x^3-x^4)x^3/((1-2x)(1+x)(1-2x^2)(1+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 08 2008]
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CROSSREFS
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Cf. A018240 = number of rational knots, A005418 = number of rational knots and links, A001045 = Jacobsthal sequence, A090597 = conjecture about sequence of rational links with n crossings.
Sequence in context: A036538 A108742 A018240 this_sequence A054272 A129016 A099163
Adjacent sequences: A090593 A090594 A090595 this_sequence A090597 A090598 A090599
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KEYWORD
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easy,nonn
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AUTHOR
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Thomas A. Gittings (tomgittings(AT)aol.com), Dec 11 2003
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