0,2

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

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 20 ).

Also the Engel expansion of exp^(1/6); cf. A006784 for the Engel expansion definition - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 03 2002

Coordination sequence for 2-dimensional cyclotomic lattice Z[zeta_6].

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.

T. D. Noe, Table of n, a(n) for n=0..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))

William A. Stein, The modular forms database

Index entries for sequences related to A2 = hexagonal = triangular lattice

G.f.: (1+4*x+x^2)/(1-x)^2.

Equals binomial transform of [1, 5, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 08 2008

G.f.: F(3,-2;1;-x/(1-x)); [From Paul Barry (pbarry(AT)wit.ie), Sep 18 2008]

[ seq(6*n, n=0..45) ]; # (except for initial term)

(PARI) a(n)=6*n+(!n)

A008458(n)=A003215(n)-A003215(n-1), n>0.

Essentially the same as A008588.

Sequence in context: A044891 A121827 A126798 this_sequence A008588 A078596 A085129

Adjacent sequences: A008455 A008456 A008457 this_sequence A008459 A008460 A008461

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).