A342179 - OEIS

%I #14 Mar 11 2021 02:13:51

%S 1,2,3,4,6,6,7,9,9,9,11,12,14,14,16,17,17,16,18,19,22,21,23,23,25,27,

%T 27,29,31,31,32,33,33,34,34,33,35,35,37,37,39,40,42,42,45,45,47,47,48,

%U 48,49,50,52,52,54,55,56,56,56,58,60,60,61,61,60,61,62,63

%N a(n) = number of nodes of degree 3 or 4 that are at distance n from the origin in the graph of the variant of the Rick Kenyon tiling where we tile a half-quadrant with L-tiles and backward-L tiles.

%C There is a unique way to tile the half-quadrant X with L-tiles and backward-L tiles:

%C                        |       .

%C                        |     .

%C                        |   .     X

%C                        | .

%C             -----------+-----------

%C                        |

%C                        |

%C                        |

%C                        |

%C - let B denote the bottom two squares of a tile and t the top square of a tile,

%C - let e denote an empty square and s denote the rightmost empty square,

%C - the bottom row T_0 can be represented as the infinite word rB*,

%C - for any k > 0, the row T_k can be build from the lower row T_{k-1} by applying the following substitutions from left to right:

%C         e -> e

%C         st -> es

%C         sB -> est

%C         tt -> B

%C         tB -> Bt

%C         Bt -> tB

%C         BB -> tBt

%H Rémy Sigrist, <a href="/A342179/b342179.txt">Table of n, a(n) for n = 0..5000</a>

%H Rémy Sigrist, <a href="/A342179/a342179.png">Illustration of initial terms</a>

%H Rémy Sigrist, <a href="/A342179/a342179_1.png">Colored representation of the nodes at distance <= 500 from the origin</a> (the color is a function of the distance)

%H Rémy Sigrist, <a href="/A342179/a342179.txt">C# program for A342179</a>

%H <a href="/index/Con#coordination_sequences">Index entries for coordination sequences</a>

%e See illustration in Links section.

%o (C#) See Links section.

%Y Cf. A341291, A341292, A342169.

%K nonn

%O 0,2

%A _Rémy Sigrist_, Mar 04 2021