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%I #15 Jan 19 2021 19:30:46
%S 29153,109649,486385,2024613,8634049,36481021,154687133,655020765,
%T 2775107981,11754906113,49795616797,210935942361,893541701545,
%U 3785099002297,16033943772281,67920864283629,287717416776137,1218790505711045,5162879481166789,21870308363154597
%N Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of four 4-gonal polygonal components chained with string components of length l as l 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>, J. Integer Seq. 12 (2009), no. 1, Article 09.1.7, 23 pp.
%F Conjectures from _Colin Barker_, Jul 09 2020: (Start)
%F G.f.: x*(29153 + 22190*x - 17480*x^2 - 4977*x^3) / ((1 + x - x^2)*(1 - 4*x - x^2)).
%F a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4) for n>4.
%F (End)
%p with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, k, m: k:=4: m:=2: F := t -> fibonacci(t): L := t -> fibonacci(t-1)+fibonacci(t+1): aa := (m, n) -> L(2*m)*F(n-2)+F(2*m+2)*F(n-1): b := (m, n) -> L(2*m)*F(n-1)+F(2*m+2)*F(n): c := (m, n) -> F(2*m+2)*F(n-2)+F(m+2)^2*F(n-1): d := (m, n) -> F(2*m+2)*F(n-1)+F(m+2)^2*F(n): lambda := (m,n) -> (d(m, n)+aa(m, n)+sqrt((d(m, n)-aa(m, n))^2+4*b(m, n)*c(m, n)))*(1/2): delta := (m,n) -> (d(m, n)+aa(m, n)-sqrt((d(m, n)-aa(m, n))^2+4*b(m, n)*c(m, n)))*(1/2): R := (m,n) -> ((lambda(m, n)-d(m, n))*L(2*m)+b(m, n)*F(2*m+2))/(2*lambda(m, n)-d(m, n)-aa(m, n)): S := (m,n) -> ((lambda(m, n)-aa(m, n))*L(2*m)-b(m, n)*F(2*m+2))/(2*lambda(m, n)-d(m, n)-aa(m, n)): simplify(R(m, n)*lambda(m, n)^(k-1)+S(m, n)*delta(m, n)^(k-1)); end proc;
%Y Cf. A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934.
%K nonn
%O 1,1
%A _Steven Schlicker_, Dec 15 2008
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