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A168113 First differences of A168112. 3


%S 1,1,2,3,3,3,6,7,6,3,6,7,8,9,16,17,10,3,6,7,8,9,16,17,12,9,16,19,22,

%T 31,46,41,18,3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,20,9,16,19,22,31,

%U 46,43,30,31,48

%N First differences of A168112.

%C a(n) is the number of toothpicks added at the n-th round in the toothpick structure of A168112.

%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 Observation: It appears that a(2^i+2) = 3, for i>0.

%F a(n) = A160731(n)/2. [From _Nathaniel Johnston_, Mar 28 2011]

%e If written as a triangle, begins:

%e 1;

%e 1;

%e 2;

%e 3,3;

%e 3,6,7,6;

%e 3,6,7,8,9,16,17,10;

%e 3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,18;

%e Rows converge to A168114.

%Y Cf. A139250, A139251, A152978, A152980, A160407, A168112, A168114.

%K nonn,tabf

%O 1,3

%A _Omar E. Pol_, Dec 07 2009

%E Terms after a(34) from _Nathaniel Johnston_, Mar 28 2011

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)