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A301718

Coordination sequence for node of type V2 in "kre" 2-D tiling (or net).

1, 5, 11, 17, 23, 28, 33, 39, 45, 51, 56, 61, 67, 73, 79, 84, 89, 95, 101, 107, 112, 117, 123, 129, 135, 140, 145, 151, 157, 163, 168, 173, 179, 185, 191, 196, 201, 207, 213, 219, 224, 229, 235, 241, 247, 252, 257, 263, 269, 275, 280, 285, 291, 297, 303, 308

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Linear recurrence and g.f. confirmed by Shutov/Maleev link. - Ray Chandler, Aug 30 2023

REFERENCES

Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 67, 1st row, 3rd tiling.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..1000

Brian Galebach, Collection of n-Uniform Tilings. See Number 18 from the list of 20 2-uniform tilings.

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

Reticular Chemistry Structure Resource (RCSR), The kre 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.

Rémy Sigrist, Illustration of first terms

Rémy Sigrist, PARI program for A301718

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

FORMULA

G.f.: (x^4+2*x^3+x^2+2*x+1)*(x+1)^2 / ((1-x)*(1-x^5)). - N. J. A. Sloane, Mar 28 2018

Conjecture: a(n) ~ 28*n/5. - Stefano Spezia, Mar 29 2023

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 5, 11, 17, 23, 28, 33}, 100] (* Paolo Xausa, Nov 16 2023 *)

PROG

(PARI) \\ See Links section.

CROSSREFS

Cf. A301716.