

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
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: A022797 A190884 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



