A160808 Toothpick sequence in Fibonacci spiral (see Comments lines for definition).

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

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