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 A301670 #35 Jun 13 2024 15:19:59
%S A301670 1,4,8,12,16,22,26,26,36,36,44,42,54,50,64,56,72,66,82,70,92,80,100,
%T A301670 86,110,94,120,100,128,110,138,114,148,124,156,130,166,138,176,144,
%U A301670 184,154,194,158,204,168,212,174,222,182,232,188,240,198,250,202,260
%N A301670 Coordination sequence for node of type V1 in "krr" 2-D tiling (or net).
%C A301670 Linear recurrence and g.f. confirmed by Shutov/Maleev link. - _Ray Chandler_, Aug 30 2023
%D A301670 Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 67, bottom row, 1st tiling.
%H A301670 Rémy Sigrist, <a href="/A301670/b301670.txt">Table of n, a(n) for n = 0..1000</a>
%H A301670 Brian Galebach, <a href="http://probabilitysports.com/tilings.html">Collection of n-Uniform Tilings</a>. See Number 7 from the list of 20 2-uniform tilings.
%H A301670 Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
%H A301670 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/krr">The krr tiling (or net)</a>
%H A301670 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 A301670 Rémy Sigrist, <a href="/A301670/a301670.png">Illustration of first terms</a>
%H A301670 Rémy Sigrist, <a href="/A301670/a301670.gp.txt">PARI program for A301670</a>
%H A301670 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,2,1,0,-1,-1).
%F A301670 Based on the b-file, the g.f. appears to be
%F A301670 (-2*x^9+x^8+5*x^7+16*x^6+21*x^5+22*x^4+19*x^3+12*x^2+5*x+1) / ((1+x)*(1-x^3)*(1-x^4)). - _N. J. A. Sloane_, Mar 25 2018
%F A301670 a(n) = (75*n + 9*(n - 4)*(-1)^n + 18*A163805(n+2) - 12*A049347(n+2))/18 for n >1. - _Stefano Spezia_, Jun 08 2024
%t A301670 LinearRecurrence[{-1,0,1,2,1,0,-1,-1},{1,4,8,12,16,22,26,26,36,36},100] (* _Paolo Xausa_, Nov 15 2023 *)
%o A301670 (PARI) \\ See Links section.
%Y A301670 Cf. A301672.
%Y A301670 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.
%Y A301670 Cf. A049347, A163805.
%K A301670 nonn,easy
%O A301670 0,2
%A A301670 _N. J. A. Sloane_, Mar 25 2018
%E A301670 More terms from _Rémy Sigrist_, Mar 25 2018