This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A047932 a(n) = floor(3*n-sqrt(12*n-3)). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) = cumulative sum of number of new penny-penny contacts when putting pennies on a table following a spiral pattern. This is the maximum possible number of contacts. a(n) is also the maximum number of times the minimum distance can occur among n points in the plane [Harborth]. REFERENCES Brass, Peter. "The maximum number of second smallest distances in finite planar sets." Discrete & Computational Geometry 7.1 (1992): 371-379. H. Harborth, Solution to problem 644A, Elemente der Mathematik (EMS Publishing House) 29, 14-15 LINKS Peter Kagey, Table of n, a(n) for n = 1..10000 K. Bezdek, M. A. Khan, Contact numbers for sphere packings, arXiv:1601.00145, Theorem 3.1. R. W. Grosse-Kunstleve, Penny Spiral Sequence MathOverflow, Maximal number of edges and triangular cells for n points in a triangular lattice, August 2011. FORMULA a(n) = floor(3*n-sqrt(12*n-3)). MATHEMATICA Table[Floor[3n-Sqrt[12n-3]], {n, 70}] (* Harvey P. Dale, Dec 25 2014 *) CROSSREFS 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*. Cf. A293956. Sequence in context: A033036 A198082 A082767 * A139130 A219087 A186705 Adjacent sequences:  A047929 A047930 A047931 * A047933 A047934 A047935 KEYWORD nonn AUTHOR EXTENSIONS Entry revised by N. J. A. Sloane, Nov 01 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 21 04:49 EDT 2018. Contains 304354 sequences. (Running on oeis4.)