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A162797 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.

%I A162797 #16 Feb 24 2021 02:48:18
%S A162797 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 A162797 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 A162797 53,81,129
%N A162797 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 A162797 It appears that a(2^k) = 1, for k >= 0. [From _Omar E. Pol_, Feb 22 2010]
%H A162797 Nathaniel Johnston, <a href="/A162797/b162797.txt">Table of n, a(n) for n = 1..94</a>
%H A162797 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 A162797 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 A162797 a(n) = A162796(n) - A162795(n).
%e A162797 Contribution from _Omar E. Pol_, Feb 22 2010: (Start)
%e A162797 If written as a triangle:
%e A162797 1;
%e A162797 1,5;
%e A162797 1,5,5,17;
%e A162797 1,5,5,17,5,17,21,49;
%e A162797 1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129;
%e A162797 1,5,5,17,5,17,21,49,5,17,21,49,21,53,81,129,5,17,21...
%e A162797 Rows converge to A173464.
%e A162797 (End)
%e A162797 Contribution from Omar E. Pol, Apr 01 2011 (Start):
%e A162797 It appears that the final terms of rows give A000337.
%e A162797 It appears that row sums give A006516.
%e A162797 (End)
%Y A162797 Cf. A139250, A139251, A159791, A159792, A162793, A162794, A162795, A162796.
%Y A162797 Cf. A000337, A058922, A173464. [From _Omar E. Pol_, Feb 22 2010]
%K A162797 nonn
%O A162797 1,3
%A A162797 _Omar E. Pol_, Jul 14 2009
%E A162797 Edited by _Omar E. Pol_, Jul 18 2009
%E A162797 More terms from _Omar E. Pol_, Feb 22 2010
%E A162797 More terms (a(51)-a(55)) from Nathaniel Johnston, Mar 30 2011