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A308896 Walk a rook along the square spiral numbered 0, 1, 2, ... (cf. A274641); a(n) = mex of earlier values the rook can move to. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
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.
LINKS
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
Rémy Sigrist, Colored representation of the spiral for -511 <= x, y <= 511 (where dark pixels correspond to higher values and red pixels correspond to 0's)
N. J. A. Sloane, Initial terms of spiral
N. J. A. Sloane, Explicit formulas for the array in A308896, Jul 02 2019
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.)
FORMULA
a(n) = 0, 1 iff n belongs to A002378, A085046, respectively. - Rémy Sigrist, Jul 02 2019
For formulas for the terms in the array, see the "Explicit formulas" link.
EXAMPLE
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]
===============================**===============================
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A039703 A171935 A103180 * A126045 A024307 A369287
KEYWORD
nonn,look
AUTHOR
N. J. A. Sloane, Jul 02 2019
EXTENSIONS
More terms from Rémy Sigrist, Jul 02 2019
STATUS
approved

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Last modified May 28 19:55 EDT 2024. Contains 372919 sequences. (Running on oeis4.)