cp's OEIS Frontend

A342285 Coordination sequence with respect to the central vertex of a dodecagon-based tiling of the plane by copies of a certain Goldberg quadrilateral tile.

%I A342285 #23 Mar 30 2021 01:14:33
%S A342285 1,6,6,18,30,36,42,54,60,66,72,78,84,90,102,108,114,120,126,132,138,
%T A342285 144,150,156,162,168,174,180,186,198,204,210,216,222,228,234,240,246,
%U A342285 252,258,264,270,276,282,288,294,300,306,312,318,324,330,336,342,348,354,360
%N A342285 Coordination sequence with respect to the central vertex of a dodecagon-based tiling of the plane by copies of a certain Goldberg quadrilateral tile.
%C A342285 There are many ways to tile the plane with the Goldberg tile; this is a particularly symmetric one.
%C A342285 In Cye Waldman's drawing, six copies of the gray sector are placed at the degree-4 vertices of the decagon, and 6 copies of a similar sector at the degree-6 vertices of the decagon.
%D A342285 Goldberg, M. (1955). “Central Tessellations,” Scripta Mathematica, 21, pp. 253-260. See Fig.7b.
%D A342285 Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987; Fig. 1.3.6(a), page 30.
%H A342285 Rémy Sigrist, <a href="/A342285/b342285.txt">Table of n, a(n) for n = 0..2500</a>
%H A342285 Rémy Sigrist, <a href="/A342285/a342285_2.png">Illustration of initial terms</a>
%H A342285 Rémy Sigrist, <a href="/A342285/a342285.gp.txt">PARI program for A342285</a>
%H A342285 N. J. A. Sloane, <a href="/A342285/a342285.pdf">Illustration of initial terms</a> (For example, the a(3) = 18 vertices at 3 steps from the center are colored blue; the a(4) = 30 vertices at 4 steps from the center are green with a black circle.)
%H A342285 Cye Waldman, <a href="/A342285/a342285_1.png">The Goldberg Tile</a>
%H A342285 Cye Waldman, <a href="/A342285/a342285.png">Central portion of tiling</a>.
%H A342285 Cye Waldman and others, Numerous postings to the Google Groups Tiling Mailing List about tilings with this Goldberg quadrilateral tile, March 2021.
%F A342285 Apparently, a(n) = 6*A138591(n-1) for n > 1. - _Rémy Sigrist_, Mar 30 2021
%o A342285 (PARI) See Links section.
%Y A342285 Cf. A138591, A250120.
%K A342285 nonn
%O A342285 0,2
%A A342285 _N. J. A. Sloane_, Mar 23 2021
%E A342285 More terms from _Rémy Sigrist_, Mar 29 2021