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A298040
Coordination sequence of Dual(4.6.12) tiling with respect to a tetravalent node.
23
1, 4, 20, 24, 40, 40, 60, 56, 80, 72, 100, 88, 120, 104, 140, 120, 160, 136, 180, 152, 200, 168, 220, 184, 240, 200, 260, 216, 280, 232, 300, 248, 320, 264, 340, 280, 360, 296, 380, 312, 400, 328, 420, 344, 440, 360, 460, 376, 480, 392, 500, 408, 520, 424, 540
OFFSET
0,2
LINKS
N. J. A. Sloane, Illustration of initial terms (shows one 90-degree quadrant 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
Conjecture: For n>0, a(n)=10n if n even, otherwise 8n.
Conjectures from Colin Barker, Apr 01 2020: (Start)
G.f.: (1 + 4*x + 18*x^2 + 16*x^3 + x^4 - 4*x^5) / ((1 - x)^2*(1 + x)^2).
a(n) = (9 + (-1)^n)*n for n>1.
a(n) = 2*a(n-2) - a(n-4) for n>5.
(End)
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {1, 4, 20, 24, 40, 40}, 60] (* Harvey P. Dale, Apr 06 2022 *)
CROSSREFS
Cf. A072154, A298041 (partial sums), A298036 (12-valent node), A298038 (hexavalent 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: A273791 A065984 A039569 * A174134 A032425 A194045
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 22 2018
EXTENSIONS
Terms a(8)-a(54) added by Tom Karzes, Apr 01 2020
STATUS
approved