A152927 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 1 as k varies.

7, 113, 1815, 29153, 468263, 7521361, 120810039, 1940481985, 31168521799, 500636830769

Offset

1,1

Links

Table of n, a(n) for n=1..10.

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 (16, 1).

Formula

Conjectures from Colin Barker, Jul 09 2020: (Start)

G.f.: x*(7 + x) / (1 - 16*x - x^2).

a(n) = 16*a(n-1) + 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:=2: l:=1: 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. A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152935.

Sequence in context: A142537 A084974 A156240 * A064330 A371328 A159552

Adjacent sequences: A152924 A152925 A152926 * A152928 A152929 A152930

Keyword

nonn,more

Author

Steven Schlicker, Dec 15 2008

Status

approved