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A308896
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Walk a rook along the square spiral numbered 0, 1, 2, ... (cf. A274641); a(n) = mex of earlier values the rook can move to.
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3
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0, 1, 0, 1, 2, 3, 0, 2, 3, 1, 2, 3, 0, 2, 3, 1, 4, 5, 6, 7, 0, 4, 5, 6, 7, 1, 4, 5, 6, 7, 0, 4, 5, 6, 7, 1, 2, 5, 4, 7, 6, 3, 0, 2, 5, 4, 7, 6, 3, 1, 2, 5, 4, 7, 6, 3, 0, 2, 5, 4, 7, 6, 3, 1, 8, 9, 10, 11, 12, 13, 14, 15, 0, 8, 9, 10, 11, 12, 13, 14, 15, 1, 8
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OFFSET
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0,5
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COMMENTS
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Analog of A308884 but using a rook rather than a knight.
The array of values - see the illustration in the link - appears to have a number of interesting symmetries.
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LINKS
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N. J. A. Sloane, The two kinds of sectors. (Rows y=1 and above form a sector of the first type, rows y=0 and below form the second type.)
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FORMULA
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For formulas for the terms in the array, see the "Explicit formulas" link.
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EXAMPLE
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The central 21 X 21 portion of the plane:
[ 4 1 3 30 31 28 29 26 27 24 25 22 23 20 21 18 19 16 17 2 0]
[ 5 2 1 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 0 3]
[18 17 16 1 3 6 7 12 13 14 15 8 9 10 11 4 5 2 0 31 30]
[19 16 17 2 1 7 6 13 12 15 14 9 8 11 10 5 4 0 3 30 31]
[16 19 18 5 4 1 3 14 15 12 13 10 11 8 9 2 0 7 6 29 28]
[17 18 19 4 5 2 1 15 14 13 12 11 10 9 8 0 3 6 7 28 29]
[22 21 20 11 10 9 8 1 3 6 7 4 5 2 0 15 14 13 12 27 26]
[23 20 21 10 11 8 9 2 1 7 6 5 4 0 3 14 15 12 13 26 27]
[20 23 22 9 8 11 10 5 4 1 3 2 0 7 6 13 12 15 14 25 24]
[21 22 23 8 9 10 11 4 5 2 1 0 3 6 7 12 13 14 15 24 25]
*26 25 24 15 14 13 12 7 6 3 *0* 1 2 5 4 11 10 9 8 23 22]
[27 24 25 14 15 12 13 6 7 0 2 3 1 4 5 10 11 8 9 22 23]
[24 27 26 13 12 15 14 3 0 4 5 6 7 1 2 9 8 11 10 21 20]
[25 26 27 12 13 14 15 0 2 5 4 7 6 3 1 8 9 10 11 20 21]
[30 29 28 7 6 3 0 8 9 10 11 12 13 14 15 1 2 5 4 19 18]
[31 28 29 6 7 0 2 9 8 11 10 13 12 15 14 3 1 4 5 18 19]
[28 31 30 3 0 4 5 10 11 8 9 14 15 12 13 6 7 1 2 17 16]
[29 30 31 0 2 5 4 11 10 9 8 15 14 13 12 7 6 3 1 16 17]
[ 6 3 0 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2]
[ 7 0 2 17 16 19 18 21 20 23 22 25 24 27 26 29 28 31 30 3 1]
[ 0 4 5 18 19 16 17 22 23 20 21 26 27 24 25 30 31 28 29 6 7]
===============================**===============================
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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