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%I A264788 #19 Nov 17 2023 11:20:42
%S A264788 2,2,4,4,6,10,10,12,16,16,18,22,22,24,28,28,30,34,34,36,40,40,42,46,
%T A264788 46,48,52,52,54,58,58,60,64,64,66,70,70,72,76,76,78,82,82,84,88,88,90,
%U A264788 94,94,96,100,100,102,106,106,108,112,112,114,118,118,120,124
%N A264788 a(n) is the number of circles added at n-th iteration of the pattern starting with 2 circles. (See comment.)
%C A264788 Pattern construction rules: (i) At n = 0, there are two circles of radius s with centers at the ends of a straight line of length s. (ii) At n > 0, draw circles by placing center at the intersection points of the circumferences of circles in the previous iteration, with overlaps forbidden. The pattern seems to be the flower of life. See illustration.
%H A264788 Colin Barker, <a href="/A264788/b264788.txt">Table of n, a(n) for n = 0..1000</a>
%H A264788 Kival Ngaokrajang, <a href="/A264788/a264788.pdf">Illustration of initial terms</a>
%H A264788 Sacred Geometry, <a href="http://www.bibliotecapleyades.net/geometria_sagrada/esp_geometria_sagrada_6.htm">Flower of Life</a>
%H A264788 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FlowerofLife.html">Flower of Life</a>
%H A264788 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A264788 From _Colin Barker_, Dec 10 2015: (Start)
%F A264788 a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.
%F A264788 G.f.: 2*(1+x^2-x^3+x^4+x^5) / ((1-x)^2*(1+x+x^2)).
%F A264788 (End)
%t A264788 LinearRecurrence[{1,0,1,-1},{2,2,4,4,6,10},100] (* _Paolo Xausa_, Nov 17 2023 *)
%o A264788 (PARI) {a = 4; print1("2, 2, ", a, ", "); for(n = 2, 100, if (Mod(n,3)==0, d1 = 2); if (Mod(n,3)==1, d1 = 4);  if (Mod(n,3)==2, d1 = 0); a = a + d1; print1(a, ", "))}
%o A264788 (PARI) Vec(2*(1+x^2-x^3+x^4+x^5)/((1-x)^2*(1+x+x^2)) + O(x^100)) \\ _Colin Barker_, Dec 10 2015
%Y A264788 Cf. A052380, A136289.
%K A264788 nonn,easy
%O A264788 0,1
%A A264788 _Kival Ngaokrajang_, Nov 25 2015

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