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Coordination sequence for node of type V2 in "usm" 2-D tiling (or net).
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%I #26 Nov 16 2023 08:44:27

%S 1,5,12,16,21,28,31,38,44,47,56,59,64,72,73,82,87,90,100,101,108,115,

%T 116,126,129,134,143,144,152,157,160,169,172,178,185,188,195,200,204,

%U 211,216,221,228,232,237,244,247,254,260,263,272,275,280,288,289,298,303,306,316,317,324,331,332,342

%N Coordination sequence for node of type V2 in "usm" 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, 2nd tiling.

%H Ray Chandler, <a href="/A301714/b301714.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 16 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/usm">The usm 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 (1,0,0,-1,2,-1,0,0,1,-1).

%F G.f.: -(-x^10-4*x^9-7*x^8-4*x^7-6*x^6-10*x^5-6*x^4-4*x^3-7*x^2-4*x-1)/(x^10-x^9+x^6-\2*x^5+x^4-x+1). - _N. J. A. Sloane_, Mar 29 2018

%t LinearRecurrence[{1,0,0,-1,2,-1,0,0,1,-1},{1,5,12,16,21,28,31,38,44,47,56},100] (* _Paolo Xausa_, Nov 16 2023 *)

%Y Cf. A301712.

%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 26 2018

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