This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A160722 Number of "ON" cells at n-th stage in a certain 2-dimensional cellular automaton based on Sierpinski triangles (see Comments for precise definition). 5
 0, 1, 5, 9, 19, 23, 33, 43, 65, 69, 79, 89, 111, 121, 143, 165, 211, 215, 225, 235, 257, 267, 289, 311, 357, 367, 389, 411, 457, 479, 525, 571, 665, 669, 679, 689, 711, 721, 743, 765, 811, 821, 843, 865, 911, 933, 979, 1025, 1119, 1129, 1151, 1173, 1219, 1241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This cellular automata is formed by the concatenation of three Sierpinski triangles, starting from a central vertex. Adjacent polygons are fused. The ON cells are triangles, but we only count after fusion. The sequence gives the number of polygons at the n-th round. If instead we start from four Sierpinski triangles we get A160720. LINKS David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.] N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS Omar E. Pol, Illustration if initial terms FORMULA a(n) = 3*A006046(n) - 2*n. - Max Alekseyev, Jan 21 2010 EXAMPLE We start at round 0 with no polygons, a(0) = 0. At round 1 we turn ON the first triangle in each of the three Sierpinski triangles. After fusion we have a concave pentagon, so a(1) = 1. At round 2 we turn ON two triangles in each the three Sierpinski triangles. After fusions we have the concave pentagon and four triangles. So a(2) = 1 + 4 = 5. CROSSREFS A160723 gives the first differences. Cf. A139250, A160720. Sequence in context: A226663 A023521 A113805 * A255652 A061202 A235799 Adjacent sequences:  A160719 A160720 A160721 * A160723 A160724 A160725 KEYWORD nonn AUTHOR Omar E. Pol, May 25 2009, Jan 03 2010 EXTENSIONS Extended by Max Alekseyev, Jan 21 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)