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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 (list; graph; refs; listen; history; text; internal format)
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 (Conway-Sloane, 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", Springer-Verlag, 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*n-21 = A017557(n-2) 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

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Last modified November 21 01:33 EST 2019. Contains 329349 sequences. (Running on oeis4.)