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 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 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 - 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

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Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)