The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 47
 7, 176, 4393, 109649, 2736832, 68311151, 1705041943, 42557737424, 1062238393657, 26513402104001, 661772814206368, 16517806953055199, 412283401012173607, 10290567218351284976, 256851897057769950793, 6411006859225897484849, 160018319583589667170432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..17. 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). 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) 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; CROSSREFS Cf. A152927, A152928, A152929, A152931, A152932, A152933, A152934, A152935. Sequence in context: A162082 A195517 A239575 * A027489 A098433 A009708 Adjacent sequences: A152927 A152928 A152929 * A152931 A152932 A152933 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.

Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)