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A160657
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The period of a 2-by-4n rectangular oscillator in the 2x2 (B36/S125) Life-like cellular automaton.
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1
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2, 6, 14, 14, 62, 126, 30, 30, 1022, 126, 4094, 2046, 1022, 32766, 62, 62, 8190, 524286, 8190, 2046, 254, 8190, 16777214, 4194302, 510, 134217726, 2097150, 1022, 1073741822, 2147483646, 126, 126, 17179869182, 8388606, 68719476734, 1022, 2097150, 2147483646
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These oscillators work and have the same period in any rule from B3/S5 to B3678/S012567.
The Nathaniel Johnston rectangular oscillator link points to Sierpinski's gasket (Pascal's triangle mod 2) as a source for the chaotic terms of A003558. This is consistent with the comment of [Sep 21 2011, A003558] showing an alternative trigonometric connection to A054142, since the latter row terms are found as alternate ascending diagonals in Pascal's triangle. - Gary W. Adamson, Sep 21 2011
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REFERENCES
| N. Johnston, The B36/S125 "2×2" Life-Like Cellular Automaton, in Game of Life Cellular Automata, A. Adamatzky (ed.), Springer-UK, 2010, pages 99-114.
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LINKS
| NathanielJohnston.com, Rectangular Oscillators in the 2*2 (B36/S125) Cellular Automaton
2x2 at LifeWiki
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FORMULA
| a(n) = 2^(A003558(n) + 1) - 2 for n >= 1.
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EXAMPLE
| a(2) = 6 because a 2-by-8 box has period 6 in this rule.
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CROSSREFS
| Cf. A054142.
Sequence in context: A091719 A054588 A084106 * A128660 A145213 A050859
Adjacent sequences: A160654 A160655 A160656 * A160658 A160659 A160660
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KEYWORD
| nonn
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AUTHOR
| Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), May 22 2009
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