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A342597
a(n) is the number of nodes of degree 3 or 4 that are at distance n from the origin in the graph of the Hofstetter-4fold tiling; a(0) = 1.
3
1, 2, 4, 6, 6, 8, 9, 11, 12, 14, 15, 18, 17, 22, 21, 22, 25, 26, 27, 31, 31, 32, 33, 34, 38, 39, 43, 42, 42, 44, 48, 50, 49, 50, 47, 54, 51, 56, 57, 59, 61, 55, 66, 67, 69, 70, 67, 72, 76, 77, 82, 81, 78, 80, 83, 83, 83, 87, 89, 93, 91, 98, 94, 97, 93, 99, 98
OFFSET
0,2
COMMENTS
We build the Hofstetter-4fold tiling as follows:
- H_0 corresponds to a 2 X 2 square:
+---+---+
| |
+ +
| |
+---+---+
O
- for any k >= 0, H_{k+1} is obtained by arranging 4 copies of H_k, rotated by 0, 90, 180, 270 degrees clockwise respectively, as follows:
+.......+
. 90.
+.......+ +.......+ ....+
. . .0 . . .
. . --> . ..... .
. . . . 180.
+.......+ +.......+.......+
O O .270 .
+.......+
- note that:
- the copy rotated by 0 degrees hides some squares on the copies rotated by 90 and 270 degrees,
- the copy rotated by 90 degrees hides some squares on the copy rotated by 180 degrees,
- the copy rotated by 180 degrees hides some squares on the copy rotated by 270 degrees,
- the Hofstetter-4fold tiling corresponds to the limit of H_k as k tends to infinity.
EXAMPLE
See illustration in Links section.
PROG
(C#) See Links section.
CROSSREFS
Sequence in context: A092989 A065558 A235384 * A035280 A244367 A020887
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 16 2021
STATUS
approved