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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 (list; graph; refs; listen; history; text; internal format)



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.


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.



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;


Cf. A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152935.

Sequence in context: A142537 A084974 A156240 * A064330 A159552 A228929

Adjacent sequences: A152924 A152925 A152926 * A152928 A152929 A152930




Steven Schlicker, Dec 15 2008



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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)