A282470 - OEIS

%I #53 Nov 01 2017 18:31:14

%S 0,1,9,16,40,62,102,124,204,258,338,360,440,494,606,676,916,1050,1194,

%T 1216,1296,1350,1462,1532,1772,1906,2082,2152,2392,2542,2878,3124,

%U 3844,4170,4442,4464,4544,4598,4710,4780,5020,5154,5330,5400,5640,5790,6126,6372,7092,7418,7722,7792,8032,8182,8518

%N Q-toothpick sequence with Q-toothpicks of radius 1 and 2 (see Comments for precise definition).

%C For the construction of this sequence we use the same the rules of A187210 (the Q-toothpick sequence) except that for the even-indexed generations here we use Q-toothpicks of radius 2, not 1.

%C The result is that the structure looks like an arrangement of ovals.

%C On the infinite square grid at stage 0 we start with no Q-toothpicks, so a(0) = 0.

%C For n >= 1, a(n) is the ratio between the total length of the lines of the structure after n-th stages and the length of a single Q-toothpick of radius 1.

%C A187210(n) gives the total number of Q-toothpicks in the structure after n-th stages.

%C A187211(n) gives the number of Q-toothpicks added at n-th stage.

%C Note that since the radius of the Q-toothpicks can be two distincts numbers so we can write an infinite number of sequences from cellular automata of this kind.

%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 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%Y Cf. A282471 (essentially the first differences).

%Y Cf. A187210 (Q-toothpick sequence).

%Y Cf. A139250, A187212, A267694, A267698.

%K nonn

%O 0,3

%A _Omar E. Pol_, Feb 16 2017