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A151723
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Total number of ON states after n generations of cellular automaton based on hexagons.
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14
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0, 1, 7, 13, 31, 37, 55, 85, 127, 133, 151, 181, 235, 289, 331, 409, 499, 505, 523, 553, 607, 661, 715, 817, 967, 1069, 1111, 1189, 1327, 1489, 1603, 1789, 1975, 1981, 1999, 2029, 2083, 2137, 2191, 2293, 2443, 2545, 2599, 2701, 2875, 3097, 3295
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Analog of A151725, but here we are working on the triangular lattice (or the A_2 lattice) where each hexagonal cell has six neighbors.
A cell is turned ON if exactly one of its six neighbors is ON. An ON cell remains ON for ever.
We start with a single ON cell.
It would be nice to find a recurrence for this sequence!
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REFERENCES
| S. M. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962 (see Example 6, page 224).
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LINKS
| David Applegate and N. J. A. Sloane, Table of n, a(n) for n = 0..1025
David Applegate, The movie version
David Applegate and N. J. A. Sloane, Table of n, A151724(n), A151723(n) for n = 0..1025
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
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FORMULA
| a(n) = 6*A169780(n) - 6*n + 1 (this is simply the defintion of A169780).
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CROSSREFS
| Cf. A151724, A151725, A147562, A170898, A170905.
Sequence in context: A065764 A073473 A040084 * A046139 A023243 A087196
Adjacent sequences: A151720 A151721 A151722 * A151724 A151725 A151726
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KEYWORD
| nonn
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AUTHOR
| David Applegate and N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2009
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EXTENSIONS
| Edited by N. J. A. Sloane, Jan 10 2010
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