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

0,3

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

Table of n, a(n) for n=0..54.

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.

Sequence in context: A221856 A309273 A358627 * A067956 A270757 A203595

Adjacent sequences: A282467 A282468 A282469 * A282471 A282472 A282473

Keyword

nonn

Author

Omar E. Pol, Feb 16 2017

Status

approved