

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
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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 nth stage. See A139250 for more information about toothpick sequences.


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..255
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Nathaniel Johnston, C script for computing terms


CROSSREFS

Cf. A000045, A139250, A139251, A160426, A160427.
Sequence in context: A177732 A081339 A063551 * A099248 A082575 A284526
Adjacent sequences: A160797 A160798 A160799 * A160801 A160802 A160803


KEYWORD

nonn


AUTHOR

Omar E. Pol, May 26 2009


EXTENSIONS

Terms after a(32) from Nathaniel Johnston, Mar 30 2011


STATUS

approved



