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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 Rémy Sigrist, Table of n, a(n) for n = 0..16128 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) Rémy Sigrist, PARI program for A308896 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 Cf. A002378, A003987, A085046, A274641, A308884, A308897. Sequence in context: A039703 A171935 A103180 * A126045 A024307 A267852 Adjacent sequences:  A308893 A308894 A308895 * A308897 A308898 A308899 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 December 5 04:10 EST 2021. Contains 349530 sequences. (Running on oeis4.)