%N Q-toothpick sequence in the first quadrant.
%C At stage 0, we start with no Q-toothpicks.
%C At stage 1, we place a Q-toothpick centered at (1,0) with its endpoints at (0,0) and (1,1).
%C At stage 2, we place two Q-toothpicks.
%C The sequence gives the number of Q-toothpicks in the structure after n-th stage.
%C For more information see A187210.
%C A187213 gives the number of Q-toothpicks added at n-th stage.
%C Note that starting from (0,1), with the first Q-toothpick centered at (1,1), we have the toothpick sequence A139250.
%C 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 Nathaniel Johnston, <a href="/A187212/b187212.txt">Table of n, a(n) for n = 0..202</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 Nathaniel Johnston, <a href="http://www.nathanieljohnston.com/2011/03/the-q-toothpick-cellular-automaton/">The Q-Toothpick Cellular Automaton</a>
%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>
%F It appears that a(n) = A139250(n) - 2*A059939(n), for n >= 1. - Omar E. Pol, Mar 29 2011
%Y Cf. A139250, A160164, A187210, A187213, A187220.
%A _Omar E. Pol_, Mar 22 2011, Mar 30 2011
%E Terms after a(24) from _Nathaniel Johnston_, Mar 28 2011