

A265045


Coordination sequence for a 6.6.6 point in the 3transitive 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
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OFFSET

0,2


COMMENTS

This tiling is 3transitive but not 3uniform since the polygons are not regular. It is a common floortiling.
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.


LINKS



FORMULA

For n >= 7 all three sequences equal 4n. (For n >= 7 the nth shell contains n1 points in the interior of each quadrant plus 4 points on the axes.)
a(n) = 2*a(n1)a(n2) for n>8.
a(n) = 4*n for n>6.
G.f.: (1+x)*(1+2*x^22*x^3+x^4+x^6x^7) / (1x)^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^22*x^3+x^4+x^6x^7)/(1x)^2 + O(x^100)) \\ Colin Barker, Jan 01 2016


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



