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A187212 Q-toothpick sequence in the first quadrant. 7


%S 0,1,3,5,9,13,21,31,39,43,51,63,75,91,119,149,165,169,177,189,201,217,

%T 245,277,297,313,341,377,417,477,565,643,675,679,687,699,711,727,755,

%U 787,807,823,851,887,927,987,1075

%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.

%K nonn,changed

%O 0,3

%A _Omar E. Pol_, Mar 22 2011, Mar 30 2011

%E Terms after a(24) from _Nathaniel Johnston_, Mar 28 2011

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)