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A187212
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Q-toothpick sequence in the first quadrant.
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8
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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
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0,3
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COMMENTS
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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
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LINKS
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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
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FORMULA
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It appears that a(n) = A139250(n) - 2*A059939(n), for n >= 1. - Omar E. Pol, Mar 29 2011
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CROSSREFS
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Cf. A139250, A160164, A187210, A187213, A187220.
Sequence in context: A227565 A136252 A354788 * A141325 A248604 A146905
Adjacent sequences: A187209 A187210 A187211 * A187213 A187214 A187215
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol, Mar 22 2011, Mar 30 2011
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EXTENSIONS
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Terms after a(24) from Nathaniel Johnston, Mar 28 2011
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STATUS
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approved
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