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A160722
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Number of "ON" cells at n-th stage in a certain 2-dimensional cellular automaton based on Sierpinski triangles (see Comments for precise definition).
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5
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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; internal format)
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OFFSET
| 0,3
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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.
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LINKS
| David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Omar E. Pol, Illustration if initial terms
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FORMULA
| a(n) = 3*A006046(n) - 2*n [From Max Alekseyev (maxale(AT)gmail.com), Jan 21 2010]
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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 non-convex pentagon, so a(1) = 1.
At round 2 we turn ON two triangles in each the three Sierpinski triangles. After fusions we have the central pentagon and four triangles. So a(2) = 1 + 4 = 5.
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CROSSREFS
| A160723 gives the first differences.
Cf. A139250, A160720.
Sequence in context: A046590 A023521 A113805 * A061202 A060161 A082674
Adjacent sequences: A160719 A160720 A160721 * A160723 A160724 A160725
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), May 25 2009, Jan 03 2010
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EXTENSIONS
| Extended by Max Alekseyev (maxale(AT)gmail.com), Jan 21 2010
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