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 A035019 #25 Nov 06 2023 07:15:13 %S A035019 1,6,6,6,12,6,6,12,6,12,12,6,6,12,12,6,12,12,12,6,18,12,12,12,12,6,12, %T A035019 12,6,12,12,6,12,24,12,12,6,12,6,12,12,12,12,6,12,12,12,24,12,6,18,12, %U A035019 12,12,12,12,18,12,12,12,12,12,12,6,12,18,12,12,12,12 %N A035019 Sizes of successive shells in hexagonal (or A_2) lattice. %C A035019 The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice. %D A035019 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 111. %H A035019 T. D. Noe, <a href="/A035019/b035019.txt">Table of n, a(n) for n = 0..10000</a> %H A035019 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> %F A035019 Nonzero coefficients in expansion of theta_3(q)*theta_3(q^3) + theta_2(q)*theta_2(q^3). %F A035019 The corresponding powers of q are A003136. - _Robert Israel_, Jul 29 2016 %p A035019 S:=series(JacobiTheta2(0,q)*JacobiTheta2(0,q^3)+JacobiTheta3(0,q)*JacobiTheta3(0,q^3),q,1001): %p A035019 subs(0=NULL,[seq(coeff(S,q,j),j=0..1000)]); # _Robert Israel_, Jul 29 2016 %t A035019 s = EllipticTheta[2, 0, q]*EllipticTheta[2, 0, q^3] + EllipticTheta[3, 0, q]* EllipticTheta[3, 0, q^3] + O[q]^1000; CoefficientList[s, q] /. 0 -> Nothing (* _Jean-François Alcover_, Sep 19 2016, after _Robert Israel_ *) %Y A035019 Cf. A003136, A004016, A038590 (partial sums), A357112. %K A035019 nonn,easy,nice %O A035019 0,2 %A A035019 _N. J. A. Sloane_