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A152998
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Toothpick sequence on the semi-infinite square grid.
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13
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0, 1, 3, 5, 7, 11, 17, 21, 23, 27, 33, 39, 47, 61, 77, 85, 87, 91, 97, 103, 111, 125, 141, 151, 159, 173, 191, 211, 241, 285, 325, 341, 343, 347, 353, 359, 367, 381, 397, 407, 415, 429, 447, 467, 497, 541, 581, 599, 607, 621, 639
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Omar E. Pol, Oct 01 2011 (Start):
On the semi-infinite square grid, at stage 0, we start from a vertical half toothpick at [(0,0),(0,1)]. This half toothpick represents one of the two components of the first toothpick placed in the toothpick structure of A139250. Consider only the toothpicks of length 2, so a(0) = 0.
At stage 1, we place an orthogonal toothpick of length 2 centered at the end, so a(1) = 1.
In each subsequent stage, for every exposed toothpick end, place an orthogonal toothpick centered at that end.
The sequence gives the number of toothpicks after n stages. A152968 (the first differences) gives the number of toothpicks added to the structure at n-th stage.
For more information see A139250. (End)
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LINKS
| David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences
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FORMULA
| a(n) = (A139250(n+1)-1)/2.
Contribution from Omar E. Pol, Oct 01 2011 (Start):
a(n) = A139250(n+1) - A153003(n) + A153000(n-1) - 1, if n >= 1.
a(n) = A153003(n) - A153000(n-1), if n >= 1.
a(n) = 2*A153000(n-1) + 1, if n >= 1.
(End)
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CROSSREFS
| Cf. A139250, A139251, A152968.
Cf. A153000, A152978.
Sequence in context: A155779 A094342 A045397 * A108539 A170886 A090919
Adjacent sequences: A152995 A152996 A152997 * A152999 A153000 A153001
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Dec 19 2008, Dec 23 2008, Jan 02 2008
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