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A301726 Coordination sequence for node of type V2 in "kra" 2-D tiling (or net). 38
1, 5, 11, 16, 21, 27, 33, 38, 43, 49, 54, 59, 65, 70, 75, 81, 87, 92, 97, 103, 108, 113, 119, 124, 129, 135, 141, 146, 151, 157, 162, 167, 173, 178, 183, 189, 195, 200, 205, 211, 216, 221, 227, 232, 237, 243, 249, 254, 259, 265, 270, 275, 281, 286, 291, 297, 303, 308, 313, 319, 324, 329, 335, 340 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 66, 1st row, 1st tiling.
LINKS
Brian Galebach, Collection of n-Uniform Tilings. See Number 20 from the list of 20 2-uniform tilings.
Reticular Chemistry Structure Resource (RCSR), The kra tiling (or net)
A. V. Maleev, A. A. Mokrova, 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.
Anton Shutov and Andrey Maleev, Coordination sequences and layer-by-layer growth of periodic structures, Zeitschrift für Kristallographie - Crystalline Materials, Volume 234, Issue 5, Pages 291-299 (2018).
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 (2, -2, 2, -2, 2, -2, 2, -2, 2, -1).
FORMULA
G.f. = (x^2+x+1)*(x^8+2*x^7+3*x^4+2*x+1)/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2). - N. J. A. Sloane, Mar 29 2018
MATHEMATICA
CoefficientList[Series[(x^2+x+1)(x^8+2x^7+3x^4+2x+1)/((x^4+x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2), {x, 0, 110}], x] (* Harvey P. Dale, Sep 25 2020 *)
CROSSREFS
Cf. A301724.
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: A219529 A314131 A314132 * A314133 A314134 A314135
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 26 2018
EXTENSIONS
a(11)-a(100) from Davide M. Proserpio, Mar 28 2018
STATUS
approved

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Last modified June 20 10:31 EDT 2024. Contains 373516 sequences. (Running on oeis4.)