OFFSET
0,2
COMMENTS
"5-neighbor" means that each triangle has a point in common with exactly five other triangles.
This packing is actually the thinnest 5-neighbor packing in the plane using any congruent convex polygons.
More formally, this sequence is the coordination sequence of the vertex-edge graph of the packing with respect to a hexavalent vertex with three-fold rotational symmetry. The base vertex is marked "C" in the figure.
REFERENCES
William Moser and Janos Pach, Research Problems in Discrete Geometry: Packing and Covering, DIMACS Technical Report 93-32, May 1993. See Fig. 19.1a, page 32. There is an error in the figure: the triangle at the right of the bottom row should not be shaded. The figure shown here is correct.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..1000
Rémy Sigrist, Illustration of first terms
Rémy Sigrist, PARI program for A320492
N. J. A. Sloane, The packing and its graph. (The triangles are shaded, the base point is marked C, and the green dots indicate the centers of large empty triangles.)
FORMULA
Conjectures from Colin Barker, Oct 23 2018: (Start)
G.f.: (1 + 6*x + 9*x^2 + 17*x^3 + 15*x^4 + 20*x^5 + 9*x^6 + 6*x^7 + x^8) / ((1 - x)^2*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n-3) + a(n-5) - a(n-8) for n>8.
(End)
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 21 2018
EXTENSIONS
More terms from Rémy Sigrist, Oct 23 2018
STATUS
approved