A066393 Coordination sequence for (9^3, 3.9^2) net with respect to a vertex of type 9^3.

1, 3, 6, 6, 12, 15, 12, 21, 24, 18, 30, 33, 24, 39, 42, 30, 48, 51, 36, 57, 60, 42, 66, 69, 48, 75, 78, 54, 84, 87, 60, 93, 96, 66, 102, 105, 72, 111, 114, 78, 120, 123, 84, 129, 132, 90, 138, 141, 96, 147, 150, 102, 156, 159, 108, 165, 168, 114

Offset: 0

Author

N. J. A. Sloane, Dec 24 2001

Keywords

• nonn

Comments

This net may be regarded as a tiling of the plane by 9-gons and triangles. There are two kinds of vertices: (a) 9^3 vertices, where three 9-gons meet, and (b) 3.9^2 vertices, where a triangle and two 9-gons meet. The present sequence is the coordination sequence with respect to a vertex of type 9^3. See also A319980.

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..300
• Jean-Guillaume Eon, Geometrical relationships between nets mapped on isomorphic quotient graphs: examples, Journal of Solid State Chemistry 138.1 (1998): 55-65. See Fig. 1.
• Jean-Guillaume Eon, Algebraic determination of generating functions for coordination sequences in crystal structures, Acta Cryst. A58 (2002), 47-53. See Section 8.
• N. J. A. Sloane, A portion of the (9^3, 3.9^2) net

Crossrefs

Cf. A319980, A109044, A186101.

Programs

Maple

seq(coeftayl((1+3*x+6*x^2+4*x^3+6*x^4+3*x^5+x^6)/(1-x^3)^2, x = 0, k), k=0..60); # Muniru A Asiru, Feb 13 2018

Formula

G.f.: (1+3*x+6*x^2+4*x^3+6*x^4+3*x^5+x^6)/(1-x^3)^2.

a(n) = (3*n + lcm(n,3))/2, for n>=1. - Ridouane Oudra, Jan 22 2021

a(n) = 3*A186101(n), for n>=1. - Ridouane Oudra, Jun 11 2025