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A160800 Toothpick sequence in Fibonacci spiral (see Comments lines for definition). 8
0, 1, 3, 7, 9, 10, 12, 15, 16, 17, 19, 22, 25, 28, 33, 38, 40, 41, 43, 46, 48, 50, 54, 60, 65, 68, 73, 78, 80, 82, 86, 92, 93, 95, 98, 100, 102, 106, 112, 117, 120, 125, 130, 132, 134, 138, 144, 149, 153, 160, 168, 174, 182, 196 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
On the infinite square grid we draw a Fibonacci spiral starting with 2,2,4,6,10,16,... (Note that each edge has length = A000045(k)*2, for k>0). We start at stage 0 with no toothpicks. At stage 1 we place a toothpick 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. A160801 (the first differences) gives the number added at the n-th stage. See A139250 for more information about toothpick sequences.
LINKS
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
Nathaniel Johnston, C script for computing terms
CROSSREFS
Sequence in context: A177732 A081339 A063551 * A354616 A099248 A082575
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 26 2009
EXTENSIONS
Terms after a(32) from Nathaniel Johnston, Mar 30 2011
STATUS
approved

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Last modified April 23 10:07 EDT 2024. Contains 371905 sequences. (Running on oeis4.)