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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 (list; graph; refs; listen; history; text; internal format)
 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, 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: A036715 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

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Last modified September 15 12:44 EDT 2019. Contains 327078 sequences. (Running on oeis4.)