A298036 Coordination sequence of Dual(4.6.12) tiling with respect to a 12-valent node.
1, 12, 12, 36, 24, 60, 36, 84, 48, 108, 60, 132, 72, 156, 84, 180, 96, 204, 108, 228, 120, 252, 132, 276, 144, 300, 156, 324, 168, 348, 180, 372, 192, 396, 204, 420, 216, 444, 228, 468, 240, 492, 252, 516, 264, 540, 276, 564, 288, 588, 300
Offset: 0
Links
- Hakan Icoz, Table of n, a(n) for n = 0..20000
- Tom Karzes, Tiling Coordination Sequences
- N. J. A. Sloane, Illustration of initial terms (shows one 60-degree sector of tiling)
- 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]
- Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
Crossrefs
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.
Programs
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Mathematica
LinearRecurrence[{0, 2, 0, -1}, {1, 12, 12, 36, 24}, 100] (* Paolo Xausa, Jul 19 2024 *)
Formula
From Charlie Neder, Apr 22 2019: (Start)
a(n) = 6 * n * (1 + n mod 2), n > 0.
G.f.: (1 + 12*x + 10*x^2 + 12*x^3 + x^4)/(1 - x^2)^2. (End)
Extensions
a(7)-a(50) from Charlie Neder, Apr 22 2019
Comments