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

0,3

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

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: A227565 A136252 A354788 * 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