A161411 - OEIS

%I #19 Sep 01 2023 08:17:36

%S 4,12,12,36,12,36,36,108,12,36,36,108,36,108,108,324,12,36,36,108,36,

%T 108,108,324,36,108,108,324,108,324,324,972,12,36,36,108,36,108,108,

%U 324,36,108,108,324,108,324,324,972,36,108,108,324,108,324,324,972,108,324,324

%N First differences of A160410.

%C The rows of the triangle in A147582 converge to this sequence.

%C Contribution from Omar E. Pol, Mar 28 2011 (Start):

%C a(n) is the number of cells turned "ON" at n-th stage of the cellular automaton of A160410.

%C a(n) is also the number of toothpicks added at n-th stage to the toothpick structure of A160410.

%C (End)

%H Paolo Xausa, <a href="/A161411/b161411.txt">Table of n, a(n) for n = 1..10000</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>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polca024.jpg">Illustration of initial terms (Neighbors of the vertices)</a> [From _Omar E. Pol_, Nov 17 2009]

%F a(n) = A048883(n-1)*4.

%e If written as a triangle:

%e .4;

%e .12;

%e .12,36;

%e .12,36,36,108;

%e .12,36,36,108,36,108,108,324;

%t 4*3^DigitCount[Range[0,100],2,1] (* _Paolo Xausa_, Sep 01 2023 *)

%Y Cf. A139250, A139251, A160413, A160415, A160417.

%Y Cf. A000079, A048883, A147582, A160410, A160414.

%K nonn,tabf

%O 1,1

%A _Omar E. Pol_, May 20 2009, Jun 13 2009, Jun 14 2009

%E Edited by _David Applegate_ and _N. J. A. Sloane_, Jul 13 2009