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 A301720 Coordination sequence for node of type V1 in "krb" 2-D tiling (or net). 38
 1, 6, 9, 18, 21, 24, 36, 36, 39, 54, 51, 54, 72, 66, 69, 90, 81, 84, 108, 96, 99, 126, 111, 114, 144, 126, 129, 162, 141, 144, 180, 156, 159, 198, 171, 174, 216, 186, 189, 234, 201, 204, 252, 216, 219, 270, 231, 234, 288, 246, 249, 306, 261, 264, 324, 276, 279, 342, 291, 294, 360, 306, 309, 378, 321 (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 66, 1st row, 2nd tiling. LINKS Ray Chandler, Table of n, a(n) for n = 0..1000 Brian Galebach, Collection of n-Uniform Tilings. See Number 19 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 krb 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 (0,0,2,0,0,-1). FORMULA G.f.: -(-x^6-6*x^5-9*x^4-16*x^3-9*x^2-6*x-1)/(x^6-2*x^3+1). - N. J. A. Sloane, Mar 29 2018 MATHEMATICA LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 6, 9, 18, 21, 24, 36}, 100] (* Paolo Xausa, Nov 16 2023 *) CROSSREFS Cf. A301722. 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: A229354 A316069 A351851 * A316070 A020183 A320492 Adjacent sequences: A301717 A301718 A301719 * A301721 A301722 A301723 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 19 18:32 EDT 2024. Contains 373507 sequences. (Running on oeis4.)