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%I #26 Nov 16 2023 03:50:20
%S 1,4,9,12,17,22,24,30,35,36,43,48,48,56,61,60,69,74,72,82,87,84,95,
%T 100,96,108,113,108,121,126,120,134,139,132,147,152,144,160,165,156,
%U 173,178,168,186,191,180,199,204,192,212,217,204,225,230,216,238,243
%N Coordination sequence for node of type V2 in "krh" 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 67, 2nd row, 1st tiling.
%H Rémy Sigrist, <a href="/A301688/b301688.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 12 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 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 Rémy Sigrist, <a href="/A301688/a301688.png">Illustration of first terms</a>
%H Rémy Sigrist, <a href="/A301688/a301688.gp.txt">PARI program for A301688</a>
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/krh">The krh tiling (or net)</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F G.f.: -(-x^6-4*x^5-9*x^4-10*x^3-9*x^2-4*x-1)/(x^6-2*x^3+1). - _N. J. A. Sloane_, Mar 28 2018
%t LinearRecurrence[{0,0,2,0,0,-1},{1,4,9,12,17,22,24},100] (* _Paolo Xausa_, Nov 16 2023 *)
%o (PARI) See Links section.
%Y Cf. A301686.
%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 More terms from _Rémy Sigrist_, Mar 26 2018
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