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A187212 Q-toothpick sequence in the first quadrant. 8
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 (list; graph; refs; listen; history; text; internal format)
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
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.]
FORMULA
It appears that a(n) = A139250(n) - 2*A059939(n), for n >= 1. - Omar E. Pol, Mar 29 2011
CROSSREFS
Sequence in context: A227565 A136252 A354788 * A141325 A248604 A146905
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

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Last modified April 20 06:18 EDT 2024. Contains 371799 sequences. (Running on oeis4.)