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A342577
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a(n) is the number of (not necessarily connected) tiles at distance n from the leftmost tile in the Hofstetter-4fold tiling.
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3
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1, 3, 4, 6, 9, 11, 11, 13, 15, 19, 16, 20, 25, 25, 27, 27, 29, 35, 30, 34, 41, 41, 39, 41, 47, 45, 44, 48, 57, 53, 57, 55, 57, 67, 56, 62, 73, 71, 67, 69, 73, 79, 68, 76, 89, 83, 87, 83, 93, 89, 86, 90, 105, 99, 95, 97, 109, 99, 100, 104, 121, 109, 117, 111
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OFFSET
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0,2
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COMMENTS
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We build the Hofstetter-4fold tiling as follows:
- H_0 corresponds to a 2 X 2 square:
+---+---+
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+ +
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+---+---+
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,
- in this sequence we consider connected tiles (whose squares are vertically or horizontally adjacent) as well as disconnected tiles (made up of two diagonally adjacent squares).
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LINKS
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EXAMPLE
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See illustration in Links section.
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PROG
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(C#) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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