login
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.
48
7, 113, 1815, 29153, 468263, 7521361, 120810039, 1940481985, 31168521799, 500636830769
OFFSET
1,1
LINKS
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;
KEYWORD
nonn,more
AUTHOR
Steven Schlicker, Dec 15 2008
STATUS
approved