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A152931
Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of three m-gonal polygonal components chained with string components of length 2 as m varies.
47
4393, 80361, 1425131, 25671393, 459934921, 8258011407, 148150698209, 2658683875329, 47706585218947, 856070631915129, 15361490875216193, 275651271699299271, 4946357927482614361, 88758815221749418713, 1592712152944203460571, 28580061055811939151057
OFFSET
2,1
LINKS
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 (13, 104, -260, -260, 104, 13, -1).
MAPLE
with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, k, l: k:=3: l:=2: F := t -> fibonacci(t): L := t -> fibonacci(t-1)+fibonacci(t+1): aa := (n, l) -> L(2*n)*F(l-2)+F(2*n+2)*F(l-1): b := (n, l) -> L(2*n)*F(l-1)+F(2*n+2)*F(l): c := (n, l) -> F(2*n+2)*F(l-2)+F(n+2)^2*F(l-1): d := (n, l) -> F(2*n+2)*F(l-1)+F(n+2)^2*F(l): lambda := (n, l) -> (d(n, l)+aa(n, l)+sqrt((d(n, l)-aa(n, l))^2+4*b(n, l)*c(n, l)))*(1/2): delta := (n, l) -> (d(n, l)+aa(n, l)-sqrt((d(n, l)-aa(n, l))^2+4*b(n, l)*c(n, l)))*(1/2): R := (n, l) -> ((lambda(n, l)-d(n, l))*L(2*n)+b(n, l)*F(2*n+2))/(2*lambda(n, l)-d(n, l)-aa(n, l)): S := (n, l) -> ((lambda(n, l)-aa(n, l))*L(2*n)-b(n, l)*F(2*n+2))/(2*lambda(n, l)-d(n, l)-aa(n, l)): simplify(R(n, l)*lambda(n, l)^(k-1)+S(n, l)*delta(n, l)^(k-1)); end proc;
MATHEMATICA
LinearRecurrence[{13, 104, -260, -260, 104, 13, -1}, {4393, 80361, 1425131, 25671393, 459934921, 8258011407, 148150698209}, 20] (* Harvey P. Dale, Feb 18 2024 *)
KEYWORD
nonn
AUTHOR
Steven Schlicker, Dec 15 2008
STATUS
approved