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A108053
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Maximum number of diagonals of a regular n-gon that meet at a non-center point.
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1
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0, 0, 2, 2, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2
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OFFSET
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3,3
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COMMENTS
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Starting at a(13) = 2, sequence is periodic with period 30.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
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FORMULA
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a(n) = 0 if n <= 4.
For n > 4:
a(n) = 2 if n is odd or n = 6;
a(n) = 3 if n != 6 is even but not divisible by 6;
a(n) = 4 if n = 12;
a(n) = 5 if n != 12 is divisible by 6 but not 30;
a(n) = 7 if n is divisible by 30. (End)
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EXAMPLE
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In a 30-gon, there are non-center points where 7 diagonals meet, but no more than 7. Hence a(30) = 7.
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MATHEMATICA
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LinearRecurrence[PadLeft[{1}, 30], {0, 0, 2, 2, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5}, 120] (* Ray Chandler, Aug 27 2015 - adapted to new data by Paolo Xausa, May 15 2023 *)
PadRight[{0, 0, 2, 2, 2, 3, 2, 3, 2, 4}, 120, {2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3}] (* Harvey P. Dale, Jun 20 2021 - adapted to new data by Paolo Xausa, May 15 2023 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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a(4), a(6) and a(12) corrected by Paolo Xausa, May 11 2023
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STATUS
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approved
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