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 A298036 #44 Feb 22 2025 22:26:40
%S A298036 1,12,12,36,24,60,36,84,48,108,60,132,72,156,84,180,96,204,108,228,
%T A298036 120,252,132,276,144,300,156,324,168,348,180,372,192,396,204,420,216,
%U A298036 444,228,468,240,492,252,516,264,540,276,564,288,588,300
%N A298036 Coordination sequence of Dual(4.6.12) tiling with respect to a 12-valent node.
%C A298036 Conjecture: For n>0, a(n)=6n if n even, otherwise 12n.
%C A298036 The conjecture can easily be shown to be true: The vertices at distance 2k consist of 3k 12-valent and 3k 4-alent vertices, and the vertices at distance 2k+1 consist of 6(k+1) 6-valent and 6(k+1) 4-valent vertices. - _Charlie Neder_, Apr 22 2019
%H A298036 Hakan Icoz, <a href="/A298036/b298036.txt">Table of n, a(n) for n = 0..20000</a>
%H A298036 Tom Karzes, <a href="/A250122/a250122.html">Tiling Coordination Sequences</a>
%H A298036 N. J. A. Sloane, <a href="/A298036/a298036.png">Illustration of initial terms</a> (shows one 60-degree sector of tiling)
%H A298036 N. J. A. Sloane, <a href="/A296368/a296368_2.png">Overview of coordination sequences of Laves tilings</a> [Fig. 2.7.1 of Grünbaum-Shephard 1987 with A-numbers added and in some cases the name in the RCSR database]
%H A298036 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A298036 From _Charlie Neder_, Apr 22 2019: (Start)
%F A298036 a(n) = 6 * n * (1 + n mod 2), n > 0.
%F A298036 G.f.: (1 + 12*x + 10*x^2 + 12*x^3 + x^4)/(1 - x^2)^2. (End)
%t A298036 LinearRecurrence[{0, 2, 0, -1}, {1, 12, 12, 36, 24}, 100] (* _Paolo Xausa_, Jul 19 2024 *)
%Y A298036 Cf. A072154, A298037 (partial sums), A298038 (hexavalent node), A298040 (tetravalent node).
%Y A298036 Cf. A109043 (a(n)/6), A026741 (a(n)/12).
%Y A298036 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 A298036 nonn,easy
%O A298036 0,2
%A A298036 _N. J. A. Sloane_, Jan 22 2018
%E A298036 a(7)-a(50) from _Charlie Neder_, Apr 22 2019