A152932 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of three 6-gonal polygonal components chained with string components of length l as l varies.

32733, 80361, 215658, 559305, 1469565, 3842082, 10063989, 26342577, 68971050, 180563265, 472726053, 1237607586, 3240104013, 8482697145, 22207994730, 58141279737, 152215851789, 398506268322, 1043302960485, 2731402605825, 7150904864298, 18721311979761

Offset

1,1

Links

Table of n, a(n) for n=1..22.

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 (2, 2, -1).

Formula

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

G.f.: 9*x*(3637 + 1655*x - 1170*x^2) / ((1 + x)*(1 - 3*x + x^2)).

a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>3.

(End)

Maple

with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, k, m: k:=3: m:=3: F := t -> fibonacci(t): L := t -> fibonacci(t-1)+fibonacci(t+1): aa := (m, n) -> L(2*m)*F(n-2)+F(2*m+2)*F(n-1): b := (m, n) -> L(2*m)*F(n-1)+F(2*m+2)*F(n): c := (m, n) -> F(2*m+2)*F(n-2)+F(m+2)^2*F(n-1): d := (m, n) -> F(2*m+2)*F(n-1)+F(m+2)^2*F(n): lambda := (m, n) -> (d(m, n)+aa(m, n)+sqrt((d(m, n)-aa(m, n))^2+4*b(m, n)*c(m, n)))*(1/2): delta := (m, n) -> (d(m, n)+aa(m, n)-sqrt((d(m, n)-aa(m, n))^2+4*b(m, n)*c(m, n)))*(1/2): R := (m, n) -> ((lambda(m, n)-d(m, n))*L(2*m)+b(m, n)*F(2*m+2))/(2*lambda(m, n)-d(m, n)-aa(m, n)): S := (m, n) -> ((lambda(m, n)-aa(m, n))*L(2*m)-b(m, n)*F(2*m+2))/(2*lambda(m, n)-d(m, n)-aa(m, n)): simplify(R(m, n)*lambda(m, n)^(k-1)+S(m, n)*delta(m, n)^(k-1)); end proc;

Crossrefs

Cf. A152927, A152928, A152929, A152930, A152931, A152933, A152934, A152935.

Sequence in context: A172700 A101744 A013691 * A326382 A326389 A075966

Adjacent sequences: A152929 A152930 A152931 * A152933 A152934 A152935

Keyword

nonn

Author

Steven Schlicker, Dec 15 2008

Status

approved