OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Tom Karzes, Tiling Coordination Sequences
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]
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
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
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.
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