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 A342179 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. 2
 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, 27, 29, 31, 31, 32, 33, 33, 34, 34, 33, 35, 35, 37, 37, 39, 40, 42, 42, 45, 45, 47, 47, 48, 48, 49, 50, 52, 52, 54, 55, 56, 56, 56, 58, 60, 60, 61, 61, 60, 61, 62, 63 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS There is a unique way to tile the half-quadrant X with L-tiles and backward-L tiles:                        |       .                        |     .                        |   .     X                        | .             -----------+-----------                        |                        |                        |                        | - let B denote the bottom two squares of a tile and t the top square of a tile, - let e denote an empty square and s denote the rightmost empty square, - the bottom row T_0 can be represented as the infinite word rB*, - 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:         e -> e         st -> es         sB -> est         tt -> B         tB -> Bt         Bt -> tB         BB -> tBt LINKS Rémy Sigrist, Table of n, a(n) for n = 0..5000 Rémy Sigrist, Illustration of initial terms Rémy Sigrist, Colored representation of the nodes at distance <= 500 from the origin (the color is a function of the distance) Rémy Sigrist, C# program for A342179 EXAMPLE See illustration in Links section. PROG (C#) See Links section. CROSSREFS Cf. A341291, A341292, A342169. Sequence in context: A256999 A331857 A073138 * A214965 A134361 A142727 Adjacent sequences:  A342176 A342177 A342178 * A342180 A342181 A342182 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 04 2021 STATUS approved

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Last modified January 23 17:33 EST 2022. Contains 350514 sequences. (Running on oeis4.)