

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 halfquadrant with Ltiles and backwardL 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
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OFFSET

0,2


COMMENTS

There is a unique way to tile the halfquadrant X with Ltiles and backwardL 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_{k1} 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 * A214965 A134361 A142727
Adjacent sequences: A342176 A342177 A342178 * A342180 A342181 A342182


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Mar 04 2021


STATUS

approved



