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A170876
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Number of toothpicks after n stages of 3-D toothpick structure defined in Comments.
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5
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0, 1, 5, 21, 37, 53, 117, 197, 261, 405, 565, 789, 965, 1221, 1541, 1941, 2453, 2933, 3621, 4389, 5093, 5909, 6805, 7925, 9093, 10629, 12197, 14133, 15733, 17717, 19493, 21605, 23909, 26453, 29109, 32117, 35013, 38085, 41285
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OFFSET
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0,3
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COMMENTS
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We are in 3-D, and we are placing ordinary toothpicks, as in A139250.
We start with one toothpick in the z direction
We place toothpicks at any free end, as in A139250.
We always place new toothpicks in pairs, two perpendicular toothpicks that are perpendicular to the original toothpick
The toothpicks are always in 2 out of the 3 (x, y or z) directions.
The initial values are as follows (this should be checked!):
n:.0..1..2..3..4..5..6
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x..0..0..2..4..8..4.24 (Number added in x direction)
y..0..0..2..4..8..4.24 (Number added in y direction)
z..0..1..0..8..0..8.16 (Number added in z direction)
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...0..1..4.16.16.16.64 (Total number added at n-th stage, A170876)
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a..0..1..5.21.37.53.117 (Total so far, this sequence)
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LINKS
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EXAMPLE
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At stage 2 we have a horizontal cross, a vertical toothpick then another horizontal cross, for a total of 5 toothpicks.
Then we add 8 vertical toothpicks at the ends of the crosses and 8 horizontal toothpicks in the same planes as the crosses, for a total of 21 toothpicks.
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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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