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A160802 Toothpick sequence in Fibonacci spiral (see Comments lines for definition).

%I A160802 #10 Feb 24 2021 02:48:18
%S A160802 0,1,3,7,11,15,21,25,28,30,33,37,38,40,43,45,47,51,57,62,65,70,75,77,
%T A160802 79,81,83,86,90,93,95,98,102,106,111,119,127,131,132,134,137,140,144,
%U A160802 151,159,164,168,175,184,194,209,231,243,250
%N A160802 Toothpick sequence in Fibonacci spiral (see Comments lines for definition).
%C A160802 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...
%C A160802 The sequence gives the number of toothpicks in the Fibonacci spiral after n stages. A160803 (the first differences) gives the number added at the n-th stage. See A160800 and A139250 for more information about toothpick sequences.
%H A160802 Nathaniel Johnston, <a href="/A160802/b160802.txt">Table of n, a(n) for n = 0..256</a>
%H A160802 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 A160802 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 A160802 Nathaniel Johnston, <a href="/A160802/a160802.c.txt">C script for computing terms</a>
%Y A160802 Cf. A000045, A139250, A139251, A160426, A160427, A160800, A160801, A160803.
%K A160802 nonn
%O A160802 0,3
%A A160802 _Omar E. Pol_, May 26 2009
%E A160802 Terms after a(12) from _Nathaniel Johnston_, Mar 30 2011