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%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
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