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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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 26 2009
EXTENSIONS
Terms after a(32) from Nathaniel Johnston, Mar 30 2011
STATUS
approved