A160800 - OEIS

%I #10 Feb 24 2021 02:48:18

%S 0,1,3,7,9,10,12,15,16,17,19,22,25,28,33,38,40,41,43,46,48,50,54,60,

%T 65,68,73,78,80,82,86,92,93,95,98,100,102,106,112,117,120,125,130,132,

%U 134,138,144,149,153,160,168,174,182,196

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

%C 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...

%C 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.

%H Nathaniel Johnston, <a href="/A160800/b160800.txt">Table of n, a(n) for n = 0..255</a>

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%H Nathaniel Johnston, <a href="/A160800/a160800.c.txt">C script for computing terms</a>

%Y Cf. A000045, A139250, A139251, A160426, A160427.

%K nonn

%O 0,3

%A _Omar E. Pol_, May 26 2009

%E Terms after a(32) from _Nathaniel Johnston_, Mar 30 2011