login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 47
18, 1197, 80361, 5394960, 362185569, 24314987763, 1632363850242, 109587212856081, 7357034536009605, 493907598828348264, 33158022432323420133, 2226032671355124283287, 149442611182684237761426, 10032689243282040048565125, 673535162800540841393716209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..15.

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.

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)

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;

CROSSREFS

Cf. A152927, A152928, A152929, A152930, A152931, A152932, A152934, A152935.

Sequence in context: A033518 A333006 A064564 * A177602 A252969 A182286

Adjacent sequences:  A152930 A152931 A152932 * A152934 A152935 A152936

KEYWORD

nonn

AUTHOR

Steven Schlicker, Dec 15 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 23:40 EDT 2022. Contains 353847 sequences. (Running on oeis4.)