%I A090597
%S A090597 0,1,1,3,3,8,12,27,45,96,176,363,693,1408,2752,5547,10965,22016,43776,
%T A090597 87723,174933,350208,699392,1399467,2796885,5595136,11186176,22375083,
%U A090597 44741973,89489408
%N A090597 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)].
%C A090597 Arises from a conjecture about sequence of rational links with n crossings.
%C A090597 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
%C A090597 Comment from Slavik Jablan, Dec 26 2003: a(n) = number of rational (2-component) 
               links.
%Y A090597 This is the difference between A005418 and A090596 (or A018240).
%Y A090597 Cf. A018240 = sequence of rational knots, A005418 = number of rational 
               knots and links, A001045 = Jacobsthal sequence, A090596.
%Y A090597 Sequence in context: A123315 A052407 A105039 this_sequence A126073 A126592 
               A055057
%Y A090597 Adjacent sequences: A090594 A090595 A090596 this_sequence A090598 A090599 
               A090600
%K A090597 easy,nonn
%O A090597 3,4
%A A090597 Thomas A. Gittings (tomgittings(AT)aol.com), Dec 11 2003