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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 2-dimensional 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", Springer-Verlag, 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 (* Jean-François 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

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Last modified December 6 03:02 EST 2016. Contains 278771 sequences.