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A160800
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Toothpick sequence in Fibonacci spiral (see Comments lines for definition).
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8
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0, 1, 3, 7, 9, 10, 12, 15, 16, 17, 19, 22, 25, 28, 33, 38, 40, 41, 43, 46, 48, 50, 54, 60, 65, 68, 73, 78, 80, 82, 86, 92, 93, 95, 98, 100, 102, 106, 112, 117, 120, 125, 130, 132, 134, 138, 144, 149, 153, 160, 168, 174, 182, 196
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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 2,2,4,6,10,16,... (Note that each edge has length = A000045(k)*2, for k>0). We start at stage 0 with no toothpicks. At stage 1 we place a toothpick 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. A160801 (the first differences) gives the number added at the n-th stage. See 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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