A301299 Coordination sequence for node of type V1 in "krq" 2-D tiling (or net).

1, 4, 8, 13, 18, 22, 26, 29, 34, 40, 44, 48, 50, 55, 62, 66, 70, 71, 76, 84, 88, 92, 92, 97, 106, 110, 114, 113, 118, 128, 132, 136, 134, 139, 150, 154, 158, 155, 160, 172, 176, 180, 176, 181, 194, 198, 202, 197, 202, 216, 220, 224, 218, 223, 238, 242, 246, 239, 244, 260, 264, 268, 260, 265, 282

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link. - Ray Chandler, Aug 31 2023

References

Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 66, bottom row, 2nd tiling.

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Brian Galebach, Collection of n-Uniform Tilings. See Number 5 from the list of 20 2-uniform tilings.

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

A. V. Maleev, A. A. Mokrova, and A. V. Shutov, Coordination sequences of the 2-uniform graphs (Russian), Algebra, number theory and discrete geometry: modern problems and application of past problems (2019), Proceedings of the XVI International Conference in honor of the 80th birthday of Professor Michel Deza, 262-266.

Reticular Chemistry Structure Resource (RCSR), The krq tiling (or net)

Anton Shutov and Andrey Maleev, Coordination sequences of 2-uniform graphs, Z. Kristallogr., 235 (2020), 157-166. See supplementary material, krb, vertex u_1.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Formula

G.f.: -(-x^10-4*x^9-8*x^8-13*x^7-18*x^6-20*x^5-18*x^4-13*x^3-8*x^2-4*x-1)/(x^10-2*x^5+1). - N. J. A. Sloane, Mar 29 2018

Mathematica

LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {1, 4, 8, 13, 18, 22, 26, 29, 34, 40, 44}, 100] (* Paolo Xausa, Nov 15 2023 *)

Crossrefs

Cf. A301301.

Coordination sequences for the 20 2-uniform tilings in the order in which they appear in the Galebach catalog, together with their names in the RCSR database (two sequences per tiling): #1 krt A265035, A265036; #2 cph A301287, A301289; #3 krm A301291, A301293; #4 krl A301298, A298024; #5 krq A301299, A301301; #6 krs A301674, A301676; #7 krr A301670, A301672; #8 krk A301291, A301293; #9 krn A301678, A301680; #10 krg A301682, A301684; #11 bew A008574, A296910; #12 krh A301686, A301688; #13 krf A301690, A301692; #14 krd A301694, A219529; #15 krc A301708, A301710; #16 usm A301712, A301714; #17 krj A219529, A301697; #18 kre A301716, A301718; #19 krb A301720, A301722; #20 kra A301724, A301726.

Sequence in context: A312045 A312046 A312047 * A312048 A312049 A312050

Adjacent sequences: A301296 A301297 A301298 * A301300 A301301 A301302

Keyword

nonn

Author

N. J. A. Sloane, Mar 25 2018

Extensions

a(11)-a(100) from Davide M. Proserpio, Mar 28 2018

Status

approved