

A160802


Toothpick sequence in Fibonacci spiral (see Comments lines for definition).


5



0, 1, 3, 7, 11, 15, 21, 25, 28, 30, 33, 37, 38, 40, 43, 45, 47, 51, 57, 62, 65, 70, 75, 77, 79, 81, 83, 86, 90, 93, 95, 98, 102, 106, 111, 119, 127, 131, 132, 134, 137, 140, 144, 151, 159, 164, 168, 175, 184, 194, 209, 231, 243, 250
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OFFSET

0,3


COMMENTS

On the infinite square grid we draw a Fibonacci spiral starting with 3,3,6,9,15,24,... (Note that each edge has length = A000045(k)*3, 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. A160803 (the first differences) gives the number added at the nth stage. See A160800 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), 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, A160800, A160801, A160803.
Sequence in context: A310212 A310213 A109507 * A170888 A182838 A163094
Adjacent sequences: A160799 A160800 A160801 * A160803 A160804 A160805


KEYWORD

nonn


AUTHOR

Omar E. Pol, May 26 2009


EXTENSIONS

Terms after a(12) from Nathaniel Johnston, Mar 30 2011


STATUS

approved



