OFFSET
0,2
COMMENTS
Conjecture: For n > 0, a(n)=12n if n even, otherwise 6n.
From Keagan Boyce, May 18 2024: (Start)
It appears that
a(n) = (3*n)*(3+(-1)^n) for n > 0,
which would imply that for all even n > 0,
a(n) = (3*n)*(3+(1)) = (3*n)*(4) = 12*n,
and for all odd n > 0,
a(n) = (3*n)*(3+(-1)) = (3*n)*(2) = 6*n. (End)
LINKS
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)
a(n) = (3*n)*(3+(-1)^n) for n > 0. - Keagan Boyce, May 18 2024
MATHEMATICA
Table[(3*n)*(3+(-1)^(n)), {n, 1, 54}] (* Keagan Boyce, May 18 2024 *)
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
AUTHOR
N. J. A. Sloane, Jan 22 2018
EXTENSIONS
Terms a(8)-a(54) added by Tom Karzes, Apr 01 2020
STATUS
approved