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A265045
Coordination sequence for a 6.6.6 point in the 3-transitive tiling {4.6.6, 6.6.6, 6.6.6.6} of the plane by squares and dominoes (hexagons).
3
1, 3, 7, 11, 14, 18, 23, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232
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.
The coordination sequences with respect to the points of types 4.6.6 (labeled "C" in the illustration), 6.6.6 ("B"), 6.6.6.6 ("A") are A265046, A265045, and A008574, respectively. The present sequence is for a "B" point.
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
Sequence in context: A246170 A190694 A310206 * A310207 A189385 A310208
KEYWORD
nonn,easy
AUTHOR
STATUS
approved