OFFSET
0,2
COMMENTS
This tiling is 3-transitive but not 3-uniform since the polygons are not regular. It is a common floor-tiling.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, A portion of the 3-transitive tiling {4.6.6, 6.6.6, 6.6.6.6}
N. J. A. Sloane, A portion of the 3-transitive tiling {4.6.6, 6.6.6, 6.6.6.6} showing the three types of point
N. J. A. Sloane, Hand-drawn illustration showing a(0) to a(10)
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
For n >= 7 all three sequences equal 4n. (For n >= 7 the n-th shell contains n-1 points in the interior of each quadrant plus 4 points on the axes.)
From Colin Barker, Jan 01 2016: (Start)
a(n) = 2*a(n-1)-a(n-2) for n>8.
a(n) = 4*n for n>6.
G.f.: (1+x)*(1+2*x^2-2*x^3+x^4+x^6-x^7) / (1-x)^2.
(End)
MATHEMATICA
LinearRecurrence[{2, -1}, {1, 3, 7, 11, 14, 18, 23, 28, 32}, 60] (* Harvey P. Dale, Sep 23 2017 *)
PROG
(PARI) Vec((1+x)*(1+2*x^2-2*x^3+x^4+x^6-x^7)/(1-x)^2 + O(x^100)) \\ Colin Barker, Jan 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and Susanna Cuyler, Dec 27 2015
STATUS
approved