OFFSET
0,1
COMMENTS
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.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration of initial terms
Sacred Geometry, Flower of Life
Eric Weisstein's World of Mathematics, Flower of Life
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From Colin Barker, Dec 10 2015: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.
G.f.: 2*(1+x^2-x^3+x^4+x^5) / ((1-x)^2*(1+x+x^2)).
(End)
MATHEMATICA
LinearRecurrence[{1, 0, 1, -1}, {2, 2, 4, 4, 6, 10}, 100] (* Paolo Xausa, Nov 17 2023 *)
PROG
(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, ", "))}
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, Nov 25 2015
STATUS
approved