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%I #24 Nov 16 2023 03:50:57
%S 1,6,6,9,12,18,24,21,24,30,36,42,36,39,48,54,60,51,54,66,72,78,66,69,
%T 84,90,96,81,84,102,108,114,96,99,120,126,132,111,114,138,144,150,126,
%U 129,156,162,168,141,144,174,180,186,156,159,192,198,204,171,174,210,216,222,186,189,228,234,240
%N Coordination sequence for node of type V1 in "krf" 2-D tiling (or net).
%C Linear recurrence and g.f. confirmed by Shutov/Maleev link. - _Ray Chandler_, Aug 30 2023
%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 66, 2nd row, 1st tiling.
%H Ray Chandler, <a href="/A301690/b301690.txt">Table of n, a(n) for n = 0..1000</a>
%H Brian Galebach, <a href="http://probabilitysports.com/tilings.html">Collection of n-Uniform Tilings</a>. See Number 13 from the list of 20 2-uniform tilings.
%H Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/krf">The krf tiling (or net)</a>
%H Anton Shutov and Andrey Maleev, <a href="https://doi.org/10.1515/zkri-2020-0002">Coordination sequences of 2-uniform graphs</a>, Z. Kristallogr., 235 (2020), 157-166. See supplementary material, krb, vertex u_1.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).
%F G.f.: -(-x^10-6*x^9-6*x^8-9*x^7-12*x^6-16*x^5-12*x^4-9*x^3-6*x^2-6*x-1)/(x^10-2*x^5+1). - _N. J. A. Sloane_, Mar 29 2018
%t LinearRecurrence[{0,0,0,0,2,0,0,0,0,-1},{1,6,6,9,12,18,24,21,24,30,36},100] (* _Paolo Xausa_, Nov 16 2023 *)
%Y Cf. A301692.
%Y 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.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Mar 25 2018
%E a(11)-a(100) from _Davide M. Proserpio_, Mar 28 2018
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