This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A265036 #56 Feb 21 2025 22:34:56
%S A265036 1,4,6,7,10,14,20,24,24,23,26,34,42,44,40,37,42,54,64,64,56,51,58,74,
%T A265036 86,84,72,65,74,94,108,104,88,79,90,114,130,124,104,93,106,134,152,
%U A265036 144,120,107,122,154,174,164,136,121,138,174,196,184,152,135,154,194,218
%N A265036 Coordination sequence of 2-uniform tiling {3.4.6.4, 4.6.12} with respect to a point of type 3.4.6.4.
%C A265036 Linear recurrence and g.f. confirmed by Shutov/Maleev link. - _Ray Chandler_, Aug 31 2023
%D A265036 Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See page 67, 4th row, 3rd tiling.
%D A265036 Otto Krötenheerdt, Die homogenen Mosaike n-ter Ordnung in der euklidischen Ebene, I, II, III, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg, Math-Natur. Reihe, 18 (1969), 273-290; 19 (1970), 19-38 and 97-122. [Includes classification of 2-uniform tilings]
%D A265036 Anton Shutov and Andrey Maleev, Coordination sequences of 2-uniform graphs, Z. Kristallogr., 235 (2020), 157-166.
%H A265036 Joseph Myers, <a href="/A265036/b265036.txt">Table of n, a(n) for n = 0..20000</a>
%H A265036 Miguel Carlos Fernández-Cabo, <a href="http://dx.doi.org/10.12988/imf.2014.45103">Artisan Procedures to Generate Uniform Tilings</a>, International Mathematical Forum, Vol. 9, 2014, no. 23, 1109-1130. [Background information]
%H A265036 Brian Galebach, <a href="http://probabilitysports.com/tilings.html">Collection of n-Uniform Tilings</a>. See Number 1 from the list of 20 2-uniform tilings.
%H A265036 Brian Galebach, <a href="/A265035/a265035.png">The tiling {3.4.6.4, 4.6.12}</a>, Number 1 from list of 20 2-uniform tilings. (From the previous link)
%H A265036 Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
%H A265036 Chaim Goodman-Strauss and N. J. A. Sloane, <a href="https://doi.org/10.1107/S2053273318014481">A Coloring Book Approach to Finding Coordination Sequences</a>, Acta Cryst. A75 (2019), 121-134, also <a href="http://NeilSloane.com/doc/Cairo_final.pdf">on NJAS's home page</a>. Also <a href="http://arxiv.org/abs/1803.08530">arXiv:1803.08530</a>.
%H A265036 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/krt">The krt tiling (or net)</a>
%H A265036 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 A265036 N. J. A. Sloane, <a href="/A265035/a265035_1.png">Illustration of initial terms of A265035</a> (point of type 4.6.12)
%H A265036 N. J. A. Sloane, <a href="/A265035/a265035_2.png">Illustration of initial terms of A265036</a> (point of type 3.4.6.4)
%H A265036 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-8,10,-8,4,-1).
%F A265036 Based on the b-file, the g.f. appears to be (-2*x^9+6*x^8-8*x^7+7*x^6-2*x^5-2*x^4+5*x^3-2*x^2+1) / (x^6-4*x^5+8*x^4-10*x^3+8*x^2-4*x+1). - _N. J. A. Sloane_, Dec 14 2015
%t A265036 LinearRecurrence[{4,-8,10,-8,4,-1},{1,4,6,7,10,14,20,24,24,23},100] (* _Paolo Xausa_, Nov 15 2023 *)
%Y A265036 See A265035 for the other type of point.
%Y A265036 List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706(3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120(3.3.3.3.6), A250122 (3.12.12).
%Y A265036 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 A265036 nonn,easy
%O A265036 0,2
%A A265036 _N. J. A. Sloane_, Dec 12 2015
%E A265036 Extended by _Joseph Myers_, Dec 13 2015
%E A265036 b-file extended by _Joseph Myers_, Dec 18 2015