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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)
 OFFSET 1,1 LINKS S. Schlicker, L. Morales, and D. Schultheis, Polygonal chain sequences in the space of compact sets, JIS 12 (2009) 09.1.7. FORMULA 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. (End) MAPLE 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; CROSSREFS 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 KEYWORD nonn,more AUTHOR Steven Schlicker, Dec 15 2008 STATUS approved

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