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 A038590 #23 Mar 16 2024 11:56:33 %S A038590 1,7,13,19,31,37,43,55,61,73,85,91,97,109,121,127,139,151,163,169,187, %T A038590 199,211,223,235,241,253,265,271,283,295,301,313,337,349,361,367,379, %U A038590 385,397,409,421,433,439,451,463,475,499,511,517,535,547 %N A038590 Sizes of clusters in hexagonal lattice A_2 centered at lattice point. %C A038590 The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice. %C A038590 The sequence can be approximated by a linear function with a correction term. See link for the function and representation of the deviation. The structures in the difference function can also be set to music after scaling. Some MIDI examples are linked. - _Hugo Pfoertner_, Mar 16 2024 %D A038590 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 111. %D A038590 B. K. Teo and N. J. A. Sloane, Atomic Arrangements and Electronic Requirements for Close-Packed Circular and Spherical Clusters, Inorganic Chemistry, 25 (1986), pp. 2315-2322. See Table IV. %H A038590 Hugo Pfoertner, <a href="/A038590/b038590.txt">Table of n, a(n) for n = 0..10000</a> %H A038590 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a> %H A038590 Hugo Pfoertner, <a href="/A038590/a038590.pdf">A038590(n) - n*(30.1066 - 26.4407/n^0.0792978)</a>, Plot of difference to fit. %H A038590 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a038590.mid">Audio conversion of difference to fitted function</a>, MIDI example 1. %H A038590 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a038590_6000.mid">Audio conversion of difference to fitted function</a>, MIDI example 2, terms starting at n=6000. %H A038590 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a038590_minus.mid">Audio conversion of difference to fitted function</a>, MIDI example 3, shifted scaling. %F A038590 Unique(A038589). Or, partial sums of A035019. %Y A038590 Cf. A004016, A035019, A038161, A038589. %K A038590 nonn,easy,nice %O A038590 0,2 %A A038590 _N. J. A. Sloane_