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%I #10 Feb 24 2021 02:48:18
%S 0,1,3,7,11,15,23,35,39,40,42,45,48,52,59,67,68,70,73,76,80,85,92,97,
%T 100,105,112,120,131,144,161,173,177,182,190,197,206,211,218,227,235,
%U 239,247,255,262,270,283,297
%N Toothpick sequence in Fibonacci spiral (see Comments lines for definition).
%C 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.
%H Nathaniel Johnston, <a href="/A160808/b160808.txt">Table of n, a(n) for n = 0..256</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="/A160808/a160808.c.txt">C script for computing terms</a>
%Y Cf. A000045, A139250, A139251, A160426, A160427, A160800, A160801, A160802, A160803, A160809.
%K nonn
%O 0,3
%A _Omar E. Pol_, May 26 2009
%E Terms after a(16) from _Nathaniel Johnston_, Mar 30 2011
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