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Search: id:A090597
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| A090597 |
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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
2
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| 0, 1, 1, 3, 3, 8, 12, 27, 45, 96, 176, 363, 693, 1408, 2752, 5547, 10965, 22016, 43776, 87723, 174933, 350208, 699392, 1399467, 2796885, 5595136, 11186176, 22375083, 44741973, 89489408
(list; graph; listen)
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OFFSET
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3,4
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COMMENT
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Arises from a conjecture about sequence of rational links with n crossings.
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
Comment from Slavik Jablan, Dec 26 2003: a(n) = number of rational (2-component) links.
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CROSSREFS
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This is the difference between A005418 and A090596 (or A018240).
Cf. A018240 = sequence of rational knots, A005418 = number of rational knots and links, A001045 = Jacobsthal sequence, A090596.
Adjacent sequences: A090594 A090595 A090596 this_sequence A090598 A090599 A090600
Sequence in context: A123315 A052407 A105039 this_sequence A126073 A126592 A055057
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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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