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, Scatterplot of (x,y) such that A(x,y) has bit b set to one for b = 0..6 and -63 <= x <= 64 and -63 <= y <= 64
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
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
KEYWORD
nonn,look
AUTHOR
N. J. A. Sloane, Jul 02 2019
EXTENSIONS
More terms from Rémy Sigrist, Jul 02 2019
STATUS
approved