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A160420
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Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose skeleton is the same network as the toothpick structure of A139250 but with toothpicks of length 4.
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10
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0, 5, 13, 27, 41, 57, 85, 123, 149, 165, 193, 233, 277, 337, 429, 527, 577, 593, 621, 661, 705, 765, 857, 957, 1025, 1085, 1181, 1305, 1453, 1665, 1945, 2187, 2285, 2301, 2329, 2369, 2413, 2473, 2565, 2665, 2733, 2793, 2889, 3013, 3161, 3373, 3653, 3897, 4013
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is also the number of grid points that are covered after n-th stage by an polyedge as the toothpick structure of A139250, but with toothpicks of length 4.
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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
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FORMULA
| Conjecture: a(n) = A147614(n)+2*A139250(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 22 2010]
The above conjecture is true: each toothpick covers exactly two more grid points than the corresponding toothpick in A147614.
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EXAMPLE
| a(2)=13:
.o-o-o-o-o
.....|....
.....o....
.....|....
.....o....
.....|....
.....o....
.....|....
.o-o-o-o-o
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CROSSREFS
| Cf. A139250, A139251, A147614, A147562, A160118, A160120, A160170, A160430.
Sequence in context: A008778 A014813 A180671 * A182840 A147411 A008580
Adjacent sequences: A160417 A160418 A160419 * A160421 A160422 A160423
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), May 13 2009, May 18 2009
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EXTENSIONS
| Definition revised by N. J. A. Sloane, Jan 02 2010.
Formula verified and more terms from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Nov 13 2010
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