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 A264788 a(n) is the number of circles added at n-th iteration of the pattern starting with 2 circles. (See comment.) 3
 2, 2, 4, 4, 6, 10, 10, 12, 16, 16, 18, 22, 22, 24, 28, 28, 30, 34, 34, 36, 40, 40, 42, 46, 46, 48, 52, 52, 54, 58, 58, 60, 64, 64, 66, 70, 70, 72, 76, 76, 78, 82, 82, 84, 88, 88, 90, 94, 94, 96, 100, 100, 102, 106, 106, 108, 112, 112, 114, 118, 118, 120, 124 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A052380, A136289. Sequence in context: A325253 A143483 A323093 * A192326 A131733 A128745 Adjacent sequences: A264785 A264786 A264787 * A264789 A264790 A264791 KEYWORD nonn,easy AUTHOR Kival Ngaokrajang, Nov 25 2015 STATUS approved

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Last modified September 7 05:42 EDT 2024. Contains 375729 sequences. (Running on oeis4.)