A250124 Coordination sequence of point of type 3.3.12.4 in 4-uniform tiling {3.3.4.3.4; 3.3.4.12; 3.3.12.4; 3.4.3.12}.

1, 4, 7, 10, 15, 16, 21, 29, 28, 34, 33, 40, 48, 45, 53, 51, 59, 65, 64, 72, 68, 78, 83, 83, 89, 87, 97, 100, 102, 107, 106, 114, 119, 121, 124, 125, 132, 138, 138, 143, 144, 149, 157, 156, 162, 161, 168, 176, 173, 181, 179, 187, 193, 192, 200, 196, 206, 211, 211

Offset: 0

Author

N. J. A. Sloane, Nov 29 2014

Keywords

• nonn

Comments

This tiling appears as an example in Connelly et al. (2014), Fig. 6 (the heavy black lines in the figures here are an artifact from that figure).

For the definition of k-uniform tiling see Section 2.2 of Chapter 2 of Grünbaum and Shephard (1987).

References

• Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987.

Links

• Joseph Myers, Table of n, a(n) for n = 0..1000
• Robert Connelly, Jeffrey D. Shen, Alexander D. Smith, Ball Packings with Periodic Constraints, arXiv:1301.0664 [math.MG], 2013.
• Robert Connelly, Jeffrey D. Shen, Alexander D. Smith, Ball Packings with Periodic Constraints, Discrete Comput. Geom. 52 (2014), no. 4, 754--779. MR3279548.
• Brian Galebach, Tiling 132 (in list of 4-uniform tilings).
• Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers
• N. J. A. Sloane, A portion of the 3-uniform tiling {3.3.4.3.4; 3.3.4.12; 3.3.12.4; 3.4.3.12}. The four black dots labeled P,Q,R,S show the four types of point. The present sequence is for a point of type R.
• N. J. A. Sloane, Shows layers a(0)-a(6)

Crossrefs

Cf. A250123, A250125, A250126.

List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706(3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12).

Formula

Empirical g.f.: -(3*x^14 -4*x^12 -4*x^11 -7*x^10 -12*x^9 -14*x^8 -21*x^7 -17*x^6 -15*x^5 -15*x^4 -10*x^3 -7*x^2 -4*x -1) / ((x -1)^2*(x^4 +x^3 +x^2 +x +1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - Colin Barker, Dec 02 2014

Extensions

Galebach link from Joseph Myers, Nov 30 2014

Extended by Joseph Myers, Dec 02 2014