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A342425
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a(n) is the number of (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, 6, 6, 8, 13, 12, 14, 15, 17, 22, 21, 23, 25, 28, 29, 29, 32, 36, 37, 36, 42, 42, 40, 45, 47, 51, 51, 51, 55, 57, 57, 58, 58, 69, 66, 63, 73, 73, 72, 72, 72, 84, 75, 84, 88, 85, 87, 86, 91, 98, 94, 96, 100, 107, 103, 100, 105, 113, 110, 110, 115, 115, 114
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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 only connected tiles (whose squares are vertically or horizontally adjacent); disconnected tiles made up of two diagonally adjacent squares are counted as two distinct connected tiles.
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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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