This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047932 #32 Oct 10 2021 06:12:22
%S A047932 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,
%T A047932 60,63,65,68,71,73,76,79,81,84,87,90,92,95,98,100,103,106,109,111,114,
%U A047932 117,120,122,125,128,131,133,136,139,142,144,147,150,153,156,158,161
%N A047932 a(n) = floor(3*n-sqrt(12*n-3)).
%C A047932 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.
%C A047932 a(n) is also the maximum number of times the minimum distance can occur among n points in the plane [Harborth].
%H A047932 Peter Kagey, <a href="/A047932/b047932.txt">Table of n, a(n) for n = 1..10000</a>
%H A047932 K. Bezdek, M. A. Khan, <a href="http://arxiv.org/abs/1601.00145">Contact numbers for sphere packings</a>, arXiv:1601.00145 [math.MG], 2016, Theorem 3.1.
%H A047932 Peter Brass, <a href="https://doi.org/10.1007/BF02187849">The maximum number of second smallest distances in finite planar sets</a>, Discrete & Computational Geometry 7.1 (1992): 371-379.
%H A047932 R. W. Grosse-Kunstleve, <a href="http://web.archive.org/web/20050425075654/http://cci.lbl.gov/~rwgk/EIS/PennySpiral.html">Penny Spiral Sequence</a>
%H A047932 H. Harborth, <a href="https://www.e-periodica.ch/digbib/view?pid=edm-001%3A1974%3A29%3A%3A20#20">Solution to problem 644A</a>, Elemente der Mathematik (EMS Publishing House) 29, 14-15.
%H A047932 MathOverflow, <a href="http://mathoverflow.net/questions/73621/maximal-number-of-edges-and-triangular-cells-for-n-points-in-a-triangular-lattice">Maximal number of edges and triangular cells for n points in a triangular lattice</a>, August 2011.
%F A047932 a(n) = floor(3*n-sqrt(12*n-3)).
%t A047932 Table[Floor[3n-Sqrt[12n-3]],{n,70}] (* _Harvey P. Dale_, Dec 25 2014 *)
%Y A047932 Partial sums of A047931.
%Y A047932 A186705 is the maximum number of times the *same* distance can occur between n points in the plane, not necessarily the *minimum*.
%Y A047932 Cf. A293956.
%K A047932 nonn
%O A047932 1,3
%A A047932 _Ralf W. Grosse-Kunstleve_
%E A047932 Entry revised by _N. J. A. Sloane_, Nov 01 2017