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A187212 Q-toothpick sequence in the first quadrant.

%I A187212 #18 Feb 24 2021 02:48:19
%S A187212 0,1,3,5,9,13,21,31,39,43,51,63,75,91,119,149,165,169,177,189,201,217,
%T A187212 245,277,297,313,341,377,417,477,565,643,675,679,687,699,711,727,755,
%U A187212 787,807,823,851,887,927,987,1075
%N A187212 Q-toothpick sequence in the first quadrant.
%C A187212 At stage 0, we start with no Q-toothpicks.
%C A187212 At stage 1, we place a Q-toothpick centered at (1,0) with its endpoints at (0,0) and (1,1).
%C A187212 At stage 2, we place two Q-toothpicks.
%C A187212 The sequence gives the number of Q-toothpicks in the structure after n-th stage.
%C A187212 For more information see A187210.
%C A187212 A187213 gives the number of Q-toothpicks added at n-th stage.
%C A187212 Note that starting from (0,1), with the first Q-toothpick centered at (1,1), we have the toothpick sequence A139250.
%C A187212 Also, gullwing sequence on the semi-infinite square grid, since a "gull" is formed by two Q-toothpicks. The sequence gives the number of "gulls" (or G-toothpicks) in the structure after n-th stage. See A187220. - Omar E. Pol, Mar 30 2011
%H A187212 Nathaniel Johnston, <a href="/A187212/b187212.txt">Table of n, a(n) for n = 0..202</a>
%H A187212 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 A187212 Nathaniel Johnston, <a href="http://www.nathanieljohnston.com/2011/03/the-q-toothpick-cellular-automaton/">The Q-Toothpick Cellular Automaton</a>
%H A187212 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>
%F A187212 It appears that a(n) = A139250(n) - 2*A059939(n), for n >= 1. - Omar E. Pol, Mar 29 2011
%Y A187212 Cf. A139250, A160164, A187210, A187213, A187220.
%K A187212 nonn
%O A187212 0,3
%A A187212 _Omar E. Pol_, Mar 22 2011, Mar 30 2011
%E A187212 Terms after a(24) from _Nathaniel Johnston_, Mar 28 2011