

A194444


Dtoothpick sequence of the second kind in the first quadrant.


12



0, 1, 3, 7, 11, 15, 23, 34, 42, 46, 54, 70, 94, 106, 126, 151, 167, 171, 179, 195, 219, 247, 283, 325, 369, 389, 413, 453, 517, 549, 593, 646, 678, 682, 690, 706, 730, 758, 794, 838, 890, 932, 980, 1040, 1140, 1208, 1292, 1375, 1459, 1487, 1511, 1555
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OFFSET

0,3


COMMENTS

This cellular automaton has essentially the same rules as A194270. We start at stage 0 with no toothpicks. At stage 1, we place a Dtoothpick of length sqrt(2), in diagonal direction, at (0,0),(1,1). At stage 2, we place two toothpicks of length 1. At stage 3 we place four Dtoothpicks. And so on. The toothpicks and Dtoothpicks are connected by their endpoints. The sequence gives the number of toothpicks and Dtoothpicks in the structure after nth stage. The first differences (A194445) give the number of toothpicks or Dtoothpicks added at nth stage. It appears that the structure shows a fractal (or likefractal) behavior.
First differs from A220524 at a(13).  Omar E. Pol, Mar 23 2013


LINKS

Table of n, a(n) for n=0..51.
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) = A194434(n)/4.  Omar E. Pol, Oct 15 2011


CROSSREFS

Cf. A139250, A172310, A182838, A194270, A194432, A194434, A194440, A194442, A194445, A212008, A220524.
Sequence in context: A309274 A112714 A231348 * A220524 A169626 A160808
Adjacent sequences: A194441 A194442 A194443 * A194445 A194446 A194447


KEYWORD

nonn


AUTHOR

Omar E. Pol, Aug 24 2011


EXTENSIONS

More terms from Omar E. Pol, Mar 23 2013


STATUS

approved



