

A187212


Qtoothpick sequence in the first quadrant.


7



0, 1, 3, 5, 9, 13, 21, 31, 39, 43, 51, 63, 75, 91, 119, 149, 165, 169, 177, 189, 201, 217, 245, 277, 297, 313, 341, 377, 417, 477, 565, 643, 675, 679, 687, 699, 711, 727, 755, 787, 807, 823, 851, 887, 927, 987, 1075
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OFFSET

0,3


COMMENTS

At stage 0, we start with no Qtoothpicks.
At stage 1, we place a Qtoothpick centered at (1,0) with its endpoints at (0,0) and (1,1).
At stage 2, we place two Qtoothpicks.
The sequence gives the number of Qtoothpicks in the structure after nth stage.
For more information see A187210.
A187213 gives the number of Qtoothpicks added at nth stage.
Note that starting from (0,1), with the first Qtoothpick centered at (1,1), we have the toothpick sequence A139250.
Also, gullwing sequence on the semiinfinite square grid, since a "gull" is formed by two Qtoothpicks. The sequence gives the number of "gulls" (or Gtoothpicks) in the structure after nth stage. See A187220.  Omar E. Pol, Mar 30 2011


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..202
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
Nathaniel Johnston, The QToothpick Cellular Automaton
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

It appears that a(n) = A139250(n)  2*A059939(n), for n >= 1.  Omar E. Pol, Mar 29 2011


CROSSREFS

Cf. A139250, A160164, A187210, A187213, A187220.
Sequence in context: A320596 A227565 A136252 * A141325 A248604 A146905
Adjacent sequences: A187209 A187210 A187211 * A187213 A187214 A187215


KEYWORD

nonn


AUTHOR

Omar E. Pol, Mar 22 2011, Mar 30 2011


EXTENSIONS

Terms after a(24) from Nathaniel Johnston, Mar 28 2011


STATUS

approved



