A250125 Coordination sequence of point of type 3.4.3.12 in 4-uniform tiling {3.3.4.3.4; 3.3.4.12; 3.3.12.4; 3.4.3.12}.

1, 4, 6, 11, 13, 15, 23, 23, 33, 30, 33, 42, 41, 54, 46, 54, 58, 58, 73, 64, 75, 74, 79, 89, 81, 94, 92, 100, 105, 102, 110, 109, 119, 123, 123, 126, 130, 135, 140, 142, 144, 151, 151, 161, 158, 161, 170, 169, 182, 174, 182, 186, 186, 201, 192, 203, 202, 207, 217

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 S.
• N. J. A. Sloane, Shows layers a(0)-a(6)

Crossrefs

Cf. A250123, A250124, 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.: -(x^17 +x^16 +x^15 +x^14 -2*x^13 -4*x^12 -6*x^11 -7*x^10 -11*x^9 -18*x^8 -16*x^7 -19*x^6 -14*x^5 -13*x^4 -11*x^3 -6*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