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A301682
Coordination sequence for node of type V1 in "krg" 2-D tiling (or net).
38
1, 6, 6, 18, 18, 18, 36, 30, 30, 54, 42, 42, 72, 54, 54, 90, 66, 66, 108, 78, 78, 126, 90, 90, 144, 102, 102, 162, 114, 114, 180, 126, 126, 198, 138, 138, 216, 150, 150, 234, 162, 162, 252, 174, 174, 270, 186, 186, 288, 198, 198, 306, 210, 210, 324, 222, 222, 342, 234, 234, 360, 246, 246, 378, 258
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 66, 2nd row, 2nd tiling.
LINKS
Brian Galebach, Collection of n-Uniform Tilings. See Number 10 from the list of 20 2-uniform tilings.
Reticular Chemistry Structure Resource (RCSR), The krg 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.
FORMULA
G.f.: -(-x^6-6*x^5-6*x^4-16*x^3-6*x^2-6*x-1)/(x^6-2*x^3+1). - N. J. A. Sloane, Mar 29 2018
a(n) = 2*(7*n + n*A099837(n+3) + 3*A049347(n+2))/3 for n > 0. - Stefano Spezia, Jun 08 2024
MATHEMATICA
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 6, 6, 18, 18, 18, 36}, 100] (* Paolo Xausa, Nov 15 2023 *)
CROSSREFS
Cf. A301684.
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: A337018 A315818 A315819 * A000976 A315820 A315821
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 25 2018
EXTENSIONS
a(11)-a(100) from Davide M. Proserpio, Mar 28 2018
STATUS
approved