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 A152934 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two m-gonal polygonal components chained with string components of length 3 as m varies. 47
 289, 1962, 13429, 92025, 630730, 4323069, 29630737, 203092074, 1392013765, 9541004265, 65395016074, 448224108237, 3072173741569, 21056992082730, 144326770837525, 989230403779929, 6780286055621962, 46472771985573789, 318529117843394545, 2183231052918188010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Table of n, a(n) for n=2..21. 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. Index entries for linear recurrences with constant coefficients, signature (8, -8, 1). FORMULA Conjectures from Colin Barker, Jul 09 2020: (Start) G.f.: x^2*(289 - 350*x + 45*x^2) / ((1 - x)*(1 - 7*x + x^2)). a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3) for n>4. (End) MAPLE with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, k, l: k:=2: l:=3: 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; CROSSREFS Cf. A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152935. Sequence in context: A218766 A188186 A112077 * A332737 A156575 A296404 Adjacent sequences: A152931 A152932 A152933 * A152935 A152936 A152937 KEYWORD nonn AUTHOR Steven Schlicker, Dec 15 2008 STATUS approved

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Last modified March 3 20:15 EST 2024. Contains 370512 sequences. (Running on oeis4.)