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A152998
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Toothpick sequence on the semi-infinite square grid.
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15
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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
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history;
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internal format)
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OFFSET
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0,3
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COMMENTS
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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
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FORMULA
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a(n) = 2*A153000(n-1) + 1, if n >= 1.
(End)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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