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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

%I

%S 7,176,4393,109649,2736832,68311151,1705041943,42557737424,

%T 1062238393657,26513402104001,661772814206368,16517806953055199,

%U 412283401012173607,10290567218351284976,256851897057769950793,6411006859225897484849,160018319583589667170432

%N 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.

%H S. Schlicker, L. Morales, and D. Schultheis, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Schlicker/schlicker.html">Polygonal chain sequences in the space of compact sets</a>, JIS 12 (2009) 09.1.7.

%F Conjectures from _Colin Barker_, Jul 09 2020: (Start)

%F G.f.: x*(7 + x) / (1 - 25*x + x^2).

%F a(n) = 25*a(n-1) - a(n-2) for n>1.

%F (End)

%p 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;

%Y Cf. A152927, A152928, A152929, A152931, A152932, A152933, A152934, A152935.

%K nonn

%O 1,1

%A _Steven Schlicker_, Dec 15 2008

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Last modified January 30 12:30 EST 2023. Contains 359945 sequences. (Running on oeis4.)