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 A152933 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 6-gonal polygonal components chained with string components of length 2 as k varies. 47
 18, 1197, 80361, 5394960, 362185569, 24314987763, 1632363850242, 109587212856081, 7357034536009605, 493907598828348264, 33158022432323420133, 2226032671355124283287, 149442611182684237761426, 10032689243282040048565125, 673535162800540841393716209 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS S. Schlicker, L. Morales, and D. Schultheis, Polygonal chain sequences in the space of compact sets, J. Integer Seq. 12 (2009), no. 1, Article 09.1.7, 23 pp. FORMULA Conjectures from Colin Barker, Jul 09 2020: (Start) G.f.: 9*x*(2 - x) / (1 - 67*x - 9*x^2). a(n) = 67*a(n-1) + 9*a(n-2) for n>2. (End) MAPLE with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, m, l: m:=3: l:=2: F := n -> fibonacci(n): L := n -> fibonacci(n-1)+fibonacci(n+1): aa := (m, l) -> L(2*m)*F(l-2)+F(2*m+2)*F(l-1): b := (m, l) -> L(2*m)*F(l-1)+F(2*m+2)*F(l): c := (m, l) -> F(2*m+2)*F(l-2)+F(m+2)^2*F(l-1): d := (m, l) -> F(2*m+2)*F(l-1)+F(m+2)^2*F(l): lambda := (m, l) -> (d(m, l)+aa(m, l)+sqrt((d(m, l)-aa(m, l))^2+4*b(m, l)*c(m, l)))*(1/2): delta := (m, l) -> (d(m, l)+aa(m, l)-sqrt((d(m, l)-aa(m, l))^2+4*b(m, l)*c(m, l)))*(1/2): R := (m, l) -> ((lambda(m, l)-d(m, l))*L(2*m)+b(m, l)*F(2*m+2))/(2*lambda(m, l)-d(m, l)-aa(m, l)): S := (m, l) -> ((lambda(m, l)-aa(m, l))*L(2*m)-b(m, l)*F(2*m+2))/(2*lambda(m, l)-d(m, l)-aa(m, l)): simplify(R(m, l)*lambda(m, l)^(n-1)+S(m, l)*delta(m, l)^(n-1)); end proc; CROSSREFS Cf. A152927, A152928, A152929, A152930, A152931, A152932, A152934, A152935. Sequence in context: A033518 A333006 A064564 * A177602 A252969 A182286 Adjacent sequences:  A152930 A152931 A152932 * A152934 A152935 A152936 KEYWORD nonn AUTHOR Steven Schlicker, Dec 15 2008 STATUS approved

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Last modified May 19 23:40 EDT 2022. Contains 353847 sequences. (Running on oeis4.)