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A265046
Coordination sequence for a 4.6.6 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, 5, 8, 13, 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 "C" 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+x^3+x^4-x^5+x^6-x^7) / (1-x)^2.
(End)
PROG
(PARI) Vec((1+x)*(1+x^3+x^4-x^5+x^6-x^7)/(1-x)^2+ O(x^100)) \\ Colin Barker, Jan 01 2016
CROSSREFS
Sequence in context: A337503 A310035 A310036 * A158384 A053651 A175388
KEYWORD
nonn,easy
AUTHOR
STATUS
approved