A282470 Q-toothpick sequence with Q-toothpicks of radius 1 and 2 (see Comments for precise definition).

0, 1, 9, 16, 40, 62, 102, 124, 204, 258, 338, 360, 440, 494, 606, 676, 916, 1050, 1194, 1216, 1296, 1350, 1462, 1532, 1772, 1906, 2082, 2152, 2392, 2542, 2878, 3124, 3844, 4170, 4442, 4464, 4544, 4598, 4710, 4780, 5020, 5154, 5330, 5400, 5640, 5790, 6126, 6372, 7092, 7418, 7722, 7792, 8032, 8182, 8518

Offset: 0

Author

Omar E. Pol, Feb 16 2017

Keywords

• nonn

Comments

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.

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

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

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.

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

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

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.

Links

• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A282471 (essentially the first differences).

Cf. A187210 (Q-toothpick sequence).

Cf. A139250, A187212, A267694, A267698.