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A301718 Coordination sequence for node of type V2 in "kre" 2-D tiling (or net).

%I A301718 #34 Feb 22 2025 22:24:48
%S A301718 1,5,11,17,23,28,33,39,45,51,56,61,67,73,79,84,89,95,101,107,112,117,
%T A301718 123,129,135,140,145,151,157,163,168,173,179,185,191,196,201,207,213,
%U A301718 219,224,229,235,241,247,252,257,263,269,275,280,285,291,297,303,308
%N A301718 Coordination sequence for node of type V2 in "kre" 2-D tiling (or net).
%C A301718 Linear recurrence and g.f. confirmed by Shutov/Maleev link. - _Ray Chandler_, Aug 30 2023
%D A301718 Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987. See Table 2.2.1, page 67, 1st row, 3rd tiling.
%H A301718 Rémy Sigrist, <a href="/A301718/b301718.txt">Table of n, a(n) for n = 0..1000</a>
%H A301718 Brian Galebach, <a href="http://probabilitysports.com/tilings.html">Collection of n-Uniform Tilings</a>. See Number 18 from the list of 20 2-uniform tilings.
%H A301718 Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>
%H A301718 Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/layers/kre">The kre tiling (or net)</a>
%H A301718 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 A301718 Rémy Sigrist, <a href="/A301718/a301718.png">Illustration of first terms</a>
%H A301718 Rémy Sigrist, <a href="/A301718/a301718.gp.txt">PARI program for A301718</a>
%H A301718 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F A301718 G.f.: (x^4+2*x^3+x^2+2*x+1)*(x+1)^2 / ((1-x)*(1-x^5)). - _N. J. A. Sloane_, Mar 28 2018
%F A301718 Conjecture: a(n) ~ 28*n/5. - _Stefano Spezia_, Mar 29 2023
%t A301718 LinearRecurrence[{1,0,0,0,1,-1},{1,5,11,17,23,28,33},100] (* _Paolo Xausa_, Nov 16 2023 *)
%o A301718 (PARI) \\ See Links section.
%Y A301718 Cf. A301716.
%Y A301718 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 A301718 nonn,easy
%O A301718 0,2
%A A301718 _N. J. A. Sloane_, Mar 26 2018
%E A301718 More terms from _Rémy Sigrist_, Mar 28 2018