cp's OEIS Frontend

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.

%I A152930 #20 Jul 03 2023 10:48:55
%S A152930 7,176,4393,109649,2736832,68311151,1705041943,42557737424,
%T A152930 1062238393657,26513402104001,661772814206368,16517806953055199,
%U A152930 412283401012173607,10290567218351284976,256851897057769950793,6411006859225897484849,160018319583589667170432
%N 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.
%H A152930 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.
%H A152930 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (25, -1).
%F A152930 Conjectures from _Colin Barker_, Jul 09 2020: (Start)
%F A152930 G.f.: x*(7 + x) / (1 - 25*x + x^2).
%F A152930 a(n) = 25*a(n-1) - a(n-2) for n>1.
%F A152930 (End)
%p A152930 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 A152930 Cf. A152927, A152928, A152929, A152931, A152932, A152933, A152934, A152935.
%K A152930 nonn
%O A152930 1,1
%A A152930 _Steven Schlicker_, Dec 15 2008