

A250123


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


4



1, 5, 8, 8, 11, 17, 25, 27, 24, 30, 38, 46, 47, 44, 46, 50, 64, 68, 65, 66, 70, 80, 80, 83, 87, 91, 100, 100, 99, 99, 109, 121, 121, 119, 119, 125, 133, 139, 140, 140, 145, 153, 155, 152, 158, 166, 174, 175, 172, 174, 178, 192, 196, 193, 194, 198, 208, 208, 211
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OFFSET

0,2


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 kuniform 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, 754779. MR3279548.
Brian Galebach, Tiling 132 (in list of 4uniform tilings).
Brian Galebach, kuniform tilings (k <= 6) and their Anumbers
N. J. A. Sloane, A portion of the 3uniform 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 P.
N. J. A. Sloane, Shows layers a(0)a(6)


FORMULA

Empirical g.f.: (x+1)*(x^15 +3*x^14 4*x^11 6*x^10 7*x^9 4*x^8 7*x^7 11*x^6 9*x^5 7*x^4 4*x^3 4*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


CROSSREFS

Cf. A250124, 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).
Sequence in context: A031165 A113729 A097523 * A251687 A241992 A263176
Adjacent sequences: A250120 A250121 A250122 * A250124 A250125 A250126


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Nov 29 2014


EXTENSIONS

Galebach link from Joseph Myers, Nov 30 2014
Extended by Joseph Myers, Dec 02 2014


STATUS

approved



