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).

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.

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(8)

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+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

Cf. A008574, A265045.

Sequence in context: A337503 A310035 A310036 * A158384 A053651 A175388

Adjacent sequences: A265043 A265044 A265045 * A265047 A265048 A265049

Keyword

nonn,easy

Author

N. J. A. Sloane and Susanna Cuyler, Dec 27 2015

Status

approved