%I #16 Feb 24 2021 02:48:18

%S 1,1,5,1,5,5,17,1,5,5,17,5,17,21,49,1,5,5,17,5,17,21,49,5,17,21,49,21,

%T 53,81,129,1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129,5,17,21,49,21,

%U 53,81,129

%N a(n) = difference between the number of toothpicks of A139250 that are orthogonal to the initial toothpick and the number of toothpicks that are parallel to the initial toothpick, after n even rounds.

%C It appears that a(2^k) = 1, for k >= 0. [From _Omar E. Pol_, Feb 22 2010]

%H Nathaniel Johnston, <a href="/A162797/b162797.txt">Table of n, a(n) for n = 1..94</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>

%F a(n) = A162796(n) - A162795(n).

%e Contribution from _Omar E. Pol_, Feb 22 2010: (Start)

%e If written as a triangle:

%e 1;

%e 1,5;

%e 1,5,5,17;

%e 1,5,5,17,5,17,21,49;

%e 1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129;

%e 1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129,5,17,21...

%e Rows converge to A173464.

%e (End)

%e Contribution from Omar E. Pol, Apr 01 2011 (Start):

%e It appears that the final terms of rows give A000337.

%e It appears that row sums give A006516.

%e (End)

%Y Cf. A139250, A139251, A159791, A159792, A162793, A162794, A162795, A162796.

%Y Cf. A000337, A058922, A173464. [From _Omar E. Pol_, Feb 22 2010]

%K nonn

%O 1,3

%A _Omar E. Pol_, Jul 14 2009

%E Edited by _Omar E. Pol_, Jul 18 2009

%E More terms from _Omar E. Pol_, Feb 22 2010

%E More terms (a(51)-a(55)) from Nathaniel Johnston, Mar 30 2011