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A160808
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Toothpick sequence in Fibonacci spiral (see Comments lines for definition).
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3
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0, 1, 3, 7, 11, 15, 23, 35, 39, 40, 42, 45, 48, 52, 59, 67, 68, 70, 73, 76, 80, 85, 92, 97, 100, 105, 112, 120, 131, 144, 161, 173, 177, 182, 190, 197, 206, 211, 218, 227, 235, 239, 247, 255, 262, 270, 283, 297
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| On the infinite square grid we draw a Fibonacci spiral starting with 4,4,8,12,20,32,... (Note that each edge has length = A000045(k)*4, for k>0). We start at stage 0 with no toothpicks. At stage 1 we place a toothpick of length 2 in a orthogonal direction, in the center of the Fibonacci spiral. At stage 2 we place 2 toothpicks. And so on... The sequence gives the number of toothpicks in the Fibonacci spiral after n stages. A160809 (the first differences) gives the number added at the n-th stage. See 160800, A160802 and A139250 for more information about toothpick sequences.
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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
Nathaniel Johnston, Table of n, a(n) for n = 0..256
Nathaniel Johnston, C script for computing terms
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CROSSREFS
| Cf. A000045, A139250, A139251, A160426, A160427, A160800, A160801, A160802, A160803, A160809.
Sequence in context: A112714 A194444 A169626 * A151567 A139250 A182634
Adjacent sequences: A160805 A160806 A160807 * A160809 A160810 A160811
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), May 26 2009
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EXTENSIONS
| Terms after a(16) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Mar 30 2011
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