A152930 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 2 as k varies.

7, 176, 4393, 109649, 2736832, 68311151, 1705041943, 42557737424, 1062238393657, 26513402104001, 661772814206368, 16517806953055199, 412283401012173607, 10290567218351284976, 256851897057769950793, 6411006859225897484849, 160018319583589667170432

Offset: 1

Author

Steven Schlicker, Dec 15 2008

Keywords

• nonn

Links

• S. Schlicker, L. Morales, and D. Schultheis, Polygonal chain sequences in the space of compact sets, JIS 12 (2009) 09.1.7.
• Index entries for linear recurrences with constant coefficients, signature (25, -1).

Crossrefs

Cf. A152927, A152928, A152929, A152931, A152932, A152933, A152934, A152935.

Programs

Maple

with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, m, l: m:=2: 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.: x*(7 + x) / (1 - 25*x + x^2).

a(n) = 25*a(n-1) - a(n-2) for n>1.

(End)