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Coordination sequence for node of type V2 in "kra" 2-D tiling (or net).
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%I #26 Aug 31 2023 12:41:34

%S 1,5,11,16,21,27,33,38,43,49,54,59,65,70,75,81,87,92,97,103,108,113,

%T 119,124,129,135,141,146,151,157,162,167,173,178,183,189,195,200,205,

%U 211,216,221,227,232,237,243,249,254,259,265,270,275,281,286,291,297,303,308,313,319,324,329,335,340

%N Coordination sequence for node of type V2 in "kra" 2-D tiling (or net).

%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 66, 1st row, 1st tiling.

%H Ray Chandler, <a href="/A301726/b301726.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 20 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/kra">The kra tiling (or net)</a>

%H A. V. Maleev, A. A. Mokrova, A. V. Shutov, <a href="http://poivs.tsput.ru/conf/international/XVI/files/Conference2019M.pdf#page=262">Coordination sequences of the 2-uniform graphs</a> (Russian), Algebra, number theory and discrete geometry: modern problems and application of past problems (2019), Proceedings of the XVI International Conference in honor of the 80th birthday of Professor Michel Deza, 262-266.

%H Anton Shutov and Andrey Maleev, <a href="https://doi.org/10.1515/zkri-2018-2144">Coordination sequences and layer-by-layer growth of periodic structures</a>, Zeitschrift für Kristallographie - Crystalline Materials, Volume 234, Issue 5, Pages 291-299 (2018).

%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 (2, -2, 2, -2, 2, -2, 2, -2, 2, -1).

%F G.f. = (x^2+x+1)*(x^8+2*x^7+3*x^4+2*x+1)/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2). - _N. J. A. Sloane_, Mar 29 2018

%t CoefficientList[Series[(x^2+x+1)(x^8+2x^7+3x^4+2x+1)/((x^4+x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2),{x,0,110}],x] (* _Harvey P. Dale_, Sep 25 2020 *)

%Y Cf. A301724.

%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,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 26 2018

%E a(11)-a(100) from _Davide M. Proserpio_, Mar 28 2018