# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a298040 Showing 1-1 of 1 %I A298040 #36 Jun 08 2024 20:17:41 %S A298040 1,4,20,24,40,40,60,56,80,72,100,88,120,104,140,120,160,136,180,152, %T A298040 200,168,220,184,240,200,260,216,280,232,300,248,320,264,340,280,360, %U A298040 296,380,312,400,328,420,344,440,360,460,376,480,392,500,408,520,424,540 %N A298040 Coordination sequence of Dual(4.6.12) tiling with respect to a tetravalent node. %H A298040 Harvey P. Dale, Table of n, a(n) for n = 0..1000 %H A298040 Tom Karzes, Tiling Coordination Sequences %H A298040 N. J. A. Sloane, Illustration of initial terms (shows one 90-degree quadrant of tiling) %H A298040 N. J. A. Sloane, Overview of coordination sequences of Laves tilings [Fig. 2.7.1 of Grünbaum-Shephard 1987 with A-numbers added and in some cases the name in the RCSR database] %H A298040 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). %F A298040 Conjecture: For n>0, a(n)=10n if n even, otherwise 8n. %F A298040 Conjectures from _Colin Barker_, Apr 01 2020: (Start) %F A298040 G.f.: (1 + 4*x + 18*x^2 + 16*x^3 + x^4 - 4*x^5) / ((1 - x)^2*(1 + x)^2). %F A298040 a(n) = (9 + (-1)^n)*n for n>1. %F A298040 a(n) = 2*a(n-2) - a(n-4) for n>5. %F A298040 (End) %t A298040 LinearRecurrence[{0,2,0,-1},{1,4,20,24,40,40},60] (* _Harvey P. Dale_, Apr 06 2022 *) %Y A298040 Cf. A072154, A298041 (partial sums), A298036 (12-valent node), A298038 (hexavalent node). %Y A298040 List of coordination sequences for Laves tilings (or duals of uniform planar nets): [3,3,3,3,3.3] = A008486; [3.3.3.3.6] = A298014, A298015, A298016; [3.3.3.4.4] = A298022, A298024; [3.3.4.3.4] = A008574, A296368; [3.6.3.6] = A298026, A298028; [3.4.6.4] = A298029, A298031, A298033; [3.12.12] = A019557, A298035; [4.4.4.4] = A008574; [4.6.12] = A298036, A298038, A298040; [4.8.8] = A022144, A234275; [6.6.6] = A008458. %K A298040 nonn,easy %O A298040 0,2 %A A298040 _N. J. A. Sloane_, Jan 22 2018 %E A298040 Terms a(8)-a(54) added by _Tom Karzes_, Apr 01 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE