A194434 D-toothpick sequence of the second kind starting with a X-shaped cross formed by 4 D-toothpicks.

0, 4, 12, 28, 44, 60, 92, 136, 168, 184, 216, 280, 376, 424, 504, 604, 668, 684, 716, 780, 876, 988, 1132, 1300, 1476, 1556, 1652, 1812, 2068, 2196, 2372, 2584, 2712, 2728, 2760, 2824, 2920, 3032, 3176, 3352, 3560, 3728, 3920, 4160, 4560, 4832, 5168

Offset: 0

Author

Omar E. Pol, Sep 03 2011

Keywords

• nonn

Comments

On the infinite square grid we start with no toothpicks.

At stage 1, we place a cross as a "X", formed by 4 D-toothpicks of length sqrt(2) and centered at the origin. At stage 2, we place 8 toothpicks of length 1. At stage 3, we place 16 D-toothpicks of length sqrt(2). And so on.

The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194435) give the number of toothpicks or D-toothpicks added at n-th stage.

Apparently this cellular automaton has a fractal behavior (or fractal-like behavior) related to power of 2, similar to A194270 and very similar to A194432. The octagonal structure contains a large number of distinct closed polygonal regions. For more information see A194270, A194440 and A194442.

First differs from A220514 at a(13). - Omar E. Pol, Mar 23 2013

Observation: at least for the terms in the Data section the graph also appears to be a companion of the graph of A187210 but that could be different comparing more terms. - Omar E. Pol, Jun 24 2022

Links

• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Paolo Xausa, Animated version for n = 0..31
• Paolo Xausa, Animated version for n = 0..63
• Paolo Xausa, Illustration of initial terms for n = 0..63 (multipage PDF)
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139250, A187210, A194270, A194432, A194435, A194440, A194442, A194444, A212008, A220514.

Formula

a(n) = 4*A194444(n).

Extensions

More terms from Omar E. Pol, Mar 23 2013