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 A152932 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of three 6-gonal polygonal components chained with string components of length l as l varies. 47
 32733, 80361, 215658, 559305, 1469565, 3842082, 10063989, 26342577, 68971050, 180563265, 472726053, 1237607586, 3240104013, 8482697145, 22207994730, 58141279737, 152215851789, 398506268322, 1043302960485, 2731402605825, 7150904864298, 18721311979761 (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.: 9*x*(3637 + 1655*x - 1170*x^2) / ((1 + x)*(1 - 3*x + x^2)). a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>3. (End) MAPLE with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, k, m: k:=3: m:=3: 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; CROSSREFS Cf. A152927, A152928, A152929, A152930, A152931, A152933, A152934, A152935. Sequence in context: A172700 A101744 A013691 * A326382 A326389 A075966 Adjacent sequences:  A152929 A152930 A152931 * A152933 A152934 A152935 KEYWORD nonn AUTHOR Steven Schlicker, Dec 15 2008 STATUS approved

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Last modified January 23 07:08 EST 2022. Contains 350506 sequences. (Running on oeis4.)