A298038 Coordination sequence of Dual(4.6.12) tiling with respect to a hexavalent node.

1, 6, 24, 18, 48, 30, 72, 42, 96, 54, 120, 66, 144, 78, 168, 90, 192, 102, 216, 114, 240, 126, 264, 138, 288, 150, 312, 162, 336, 174, 360, 186, 384, 198, 408, 210, 432, 222, 456, 234, 480, 246, 504, 258, 528, 270, 552, 282, 576, 294, 600, 306, 624, 318, 648

Offset

0,2

Comments

Conjecture: For n > 0, a(n)=12n if n even, otherwise 6n.

Links

Table of n, a(n) for n=0..54.

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]

Formula

Conjectures from Colin Barker, Apr 03 2020: (Start)

G.f.: (1 + 6*x + 22*x^2 + 6*x^3 + x^4) / ((1 - x)^2*(1 + x)^2).

a(n) = 2*a(n-2) - a(n-4) for n>4.

(End)

Crossrefs

Cf. A072154, A298039 (partial sums), A298036 (12-valent node), A298040 (tetravalent node).

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.

Sequence in context: A112034 A327568 A280589 * A223751 A228745 A049319

Adjacent sequences: A298035 A298036 A298037 * A298039 A298040 A298041

Keyword

nonn

Author

N. J. A. Sloane, Jan 22 2018

Extensions

Terms a(8)-a(54) added by Tom Karzes, Apr 01 2020

Status

approved