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.
18, 1197, 80361, 5394960, 362185569, 24314987763, 1632363850242, 109587212856081, 7357034536009605, 493907598828348264, 33158022432323420133, 2226032671355124283287, 149442611182684237761426, 10032689243282040048565125, 673535162800540841393716209
Offset: 1
Keywords
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.
- Index entries for linear recurrences with constant coefficients, signature (67, 9).
Programs
-
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;
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)