

A194434


Dtoothpick sequence of the second kind starting with a Xshaped cross formed by 4 Dtoothpicks.


8



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
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OFFSET

0,2


COMMENTS

On the infinite square grid we start with no toothpicks.
At stage 1, we place a cross as a "X", formed by 4 Dtoothpicks 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 Dtoothpicks of length sqrt(2). And so on.
The sequence gives the number of toothpicks and Dtoothpicks in the structure after nth stage. The first differences (A194435) give the number of toothpicks or Dtoothpicks added at nth stage.
Apparently this cellular automaton has a fractal behavior (or likefractal 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


LINKS

Table of n, a(n) for n=0..46.
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences


FORMULA

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


CROSSREFS

Cf. A139250, A194270, A194432, A194435, A194440, A194442, A194444, A212008, A220514.
Sequence in context: A009906 A194432 A220512 * A220514 A178571 A278211
Adjacent sequences: A194431 A194432 A194433 * A194435 A194436 A194437


KEYWORD

nonn


AUTHOR

Omar E. Pol, Sep 03 2011


EXTENSIONS

More terms from Omar E. Pol, Mar 23 2013


STATUS

approved



