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A047932
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Cumulative sum of number of new penny-penny contacts when putting pennies on a table following a spiral pattern.
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2
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0, 1, 3, 5, 7, 9, 12, 14, 16, 19, 21, 24, 26, 29, 31, 34, 36, 39, 42, 44, 47, 49, 52, 55, 57, 60, 63, 65, 68, 71, 73, 76, 79, 81, 84, 87, 90, 92, 95, 98, 100, 103, 106, 109, 111, 114, 117, 120, 122, 125, 128, 131, 133, 136, 139, 142, 144, 147, 150, 153, 156, 158, 161
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OFFSET
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1,3
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COMMENTS
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This is the maximum possible number of contacts. It is also the maximum number of times the minimum distance can occur among n points in the plane.
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REFERENCES
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H. Harborth, Solution to problem 644A, Elemente der Mathematik (EMS Publishing House) 29, 14-15
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LINKS
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Table of n, a(n) for n=1..63.
R. W. Grosse-Kunstleve, Penny Spiral Sequence
http://mathoverflow.net/questions/73621/maximal-number-of-edges-and-triangular-cells-for-n-points-in-a-triangular-lattice
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FORMULA
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a(n) = floor(3*n-sqrt(12*n-3))
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CROSSREFS
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Partial sums of A047931.
A186705 is the maximum number of times the *same* distance can occur between n points in the plane, not necessarily the *minimum*.
Sequence in context: A033036 A198082 A082767 * A139130 A219087 A186705
Adjacent sequences: A047929 A047930 A047931 * A047933 A047934 A047935
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KEYWORD
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nonn
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AUTHOR
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Ralf W. Grosse-Kunstleve (rwgk(AT)cci.lbl.gov)
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STATUS
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approved
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