A342169 Consider the variant of the Rick Kenyon tiling where we tile a half-quadrant with L-tiles and backward-L tiles; a(n) is the number of tiles at distance n from the leftmost tile.

1, 1, 3, 3, 4, 4, 6, 6, 7, 7, 9, 9, 10, 10, 12, 11, 12, 12, 14, 14, 15, 15, 16, 17, 18, 18, 20, 20, 21, 21, 23, 22, 23, 23, 25, 25, 26, 26, 28, 28, 29, 29, 31, 31, 32, 32, 34, 33, 34, 34, 36, 36, 37, 37, 38, 38, 39, 39, 41, 41, 42, 42, 44, 43, 44, 44, 46, 46

Offset

0,3

Comments

See A342179 for the construction details of the tiling.

Mark the tile at the origin with the label 0, mark the tiles that share an edge with it with the label 1, the next layer with label 2, and so on. a(n) is the number of tiles with label n.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5000

Rémy Sigrist, Illustration of initial terms

Rémy Sigrist, Colored illustration of the tiles at distance <= 50 (where the color is function of the tile orientation)

Rémy Sigrist, Colored illustration of the tiles at distance <= 50 (where the color is function of the parity of the distance)

Rémy Sigrist, C# program for A342169

Example

See illustration in Links section.

Prog

(C#) See Links section.

Crossrefs

Cf. A341291, A341292, A342179.

Sequence in context: A355067 A108942 A025561 * A187321 A145814 A198465

Adjacent sequences: A342166 A342167 A342168 * A342170 A342171 A342172

Keyword

nonn

Author

Rémy Sigrist, Mar 03 2021

Status

approved