A187212 Q-toothpick sequence in the first quadrant.

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

Offset: 0

Author

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

Keywords

• nonn

Comments

At stage 0, we start with no Q-toothpicks.

At stage 1, we place a Q-toothpick centered at (1,0) with its endpoints at (0,0) and (1,1).

At stage 2, we place two Q-toothpicks.

The sequence gives the number of Q-toothpicks in the structure after n-th stage.

For more information see A187210.

A187213 gives the number of Q-toothpicks added at n-th stage.

Note that starting from (0,1), with the first Q-toothpick centered at (1,1), we have the toothpick sequence A139250.

Also, gullwing sequence on the semi-infinite square grid, since a "gull" is formed by two Q-toothpicks. The sequence gives the number of "gulls" (or G-toothpicks) in the structure after n-th 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), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
• Nathaniel Johnston, The Q-Toothpick Cellular Automaton
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A139250, A160164, A187210, A187213, A187220.

Formula

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

Extensions

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