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A160802
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Toothpick sequence in Fibonacci spiral (see Comments lines for definition).
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5
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0, 1, 3, 7, 11, 15, 21, 25, 28, 30, 33, 37, 38, 40, 43, 45, 47, 51, 57, 62, 65, 70, 75, 77, 79, 81, 83, 86, 90, 93, 95, 98, 102, 106, 111, 119, 127, 131, 132, 134, 137, 140, 144, 151, 159, 164, 168, 175, 184, 194, 209, 231, 243, 250
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OFFSET
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0,3
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COMMENTS
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On the infinite square grid we draw a Fibonacci spiral starting with 3,3,6,9,15,24,... (Note that each edge has length = A000045(k)*3, for k>0). We start at stage 0 with no toothpicks. At stage 1 we place a toothpick of length 2 in a orthogonal direction, in the center of the Fibonacci spiral. At stage 2 we place 2 toothpicks. And so on...
The sequence gives the number of toothpicks in the Fibonacci spiral after n stages. A160803 (the first differences) gives the number added at the n-th stage. See A160800 and A139250 for more information about toothpick sequences.
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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