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.

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

Offset

0,2

Comments

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

| .

| .

| . X

| .

-----------+-----------

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- 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

Index entries for coordination sequences

Example

See illustration in Links section.

Prog

(C#) See Links section.

Crossrefs

Cf. A341291, A341292, A342169.

Sequence in context: A256999 A331857 A073138 * A362813 A367964 A214965

Adjacent sequences: A342176 A342177 A342178 * A342180 A342181 A342182

Keyword

nonn

Author

Rémy Sigrist, Mar 04 2021

Status

approved