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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

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

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

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Last modified October 22 11:13 EDT 2018. Contains 316438 sequences. (Running on oeis4.)