

A035019


Sizes of successive shells in hexagonal (or A_2) lattice.


10



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, 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, 12, 12, 12, 12, 18, 12, 12, 12, 12, 12, 12, 6, 12, 18, 12, 12, 12, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

The hexagonal lattice is the familiar 2dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, p. 111.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2


FORMULA

Nonzero coefficients in expansion of theta_3(q)*theta_3(q^3)+theta_2(q)*theta_2(q^3).
The corresponding powers of q are A003136.  Robert Israel, Jul 29 2016


MAPLE

S:=series(JacobiTheta2(0, q)*JacobiTheta2(0, q^3)+JacobiTheta3(0, q)*JacobiTheta3(0, q^3), q, 1001):
subs(0=NULL, [seq(coeff(S, q, j), j=0..1000)]); # Robert Israel, Jul 29 2016


MATHEMATICA

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 (* JeanFrançois Alcover, Sep 19 2016, after Robert Israel *)


CROSSREFS

Cf. A003136, A004016.
Sequence in context: A179409 A186983 A046264 * A216057 A212096 A052380
Adjacent sequences: A035016 A035017 A035018 * A035020 A035021 A035022


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


STATUS

approved



