

A316319


Coordination sequence for a trivalent node in a chamfered version of the 3^6 triangular tiling of the plane.


2



1, 3, 7, 14, 25, 38, 51, 63, 75, 87, 99, 111, 123, 135, 147, 159, 171, 183, 195, 207, 219, 231, 243, 255, 267, 279, 291, 303, 315, 327, 339, 351, 363, 375, 387, 399, 411, 423, 435, 447, 459, 471, 483, 495, 507, 519, 531, 543, 555, 567, 579, 591, 603, 615, 627, 639
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OFFSET

0,2


COMMENTS

Let E denote the lattice of Eisenstein integers u + v*w in the plane, with each point joined to its six neighbors. Here u and v are ordinary integers and w = (1+sqrt(3))/2 is a complex cube root of unity. Let theta = w  w^2 = sqrt(3). Then theta*E is a sublattice of E of index 3 (ConwaySloane, Fig. 7.2). The tiling considered in this sequence is obtained by replacing each node in theta*E by a small hexagon.


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, 3rd. ed., 1993. See Fig. 7.2, page 199.


LINKS

Table of n, a(n) for n=0..55.
Rémy Sigrist, Illustration of initial terms
N. J. A. Sloane, The graph of the tiling. (The red dots indicate the nodes of the sublattice theta*E.)


FORMULA

a(n) = 12*n21 = A017557(n2) for n > 5.


CROSSREFS

See A316320 for hexavalent node.
See A250120 for links to thousands of other coordination sequences.
Cf. A017557.
Sequence in context: A123386 A060999 A089187 * A179178 A171973 A253895
Adjacent sequences: A316316 A316317 A316318 * A316320 A316321 A316322


KEYWORD

nonn,easy


AUTHOR

Rémy Sigrist and N. J. A. Sloane, Jul 01 2018


EXTENSIONS

Terms a(16) and beyond from Andrey Zabolotskiy, Sep 30 2019


STATUS

approved



