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A160808 Toothpick sequence in Fibonacci spiral (see Comments lines for definition). 3
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; text; internal format)
OFFSET

0,3

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.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..256

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.]

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, A160800, A160801, A160802, A160803, A160809.

Sequence in context: A194444 A220524 A169626 * A151567 A139250 A256265

Adjacent sequences:  A160805 A160806 A160807 * A160809 A160810 A160811

KEYWORD

nonn

AUTHOR

Omar E. Pol, May 26 2009

EXTENSIONS

Terms after a(16) from Nathaniel Johnston, Mar 30 2011

STATUS

approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)