A334017 Table read by antidiagonals upward: T(n,k) is the number of ways to move a chess queen from (1,1) to (n,k) in the first quadrant using only up, right, and diagonal up-left moves.

1, 1, 2, 2, 5, 10, 4, 13, 33, 63, 8, 32, 98, 240, 454, 16, 76, 269, 777, 1871, 3539, 32, 176, 702, 2295, 6420, 15314, 29008, 64, 400, 1768, 6393, 19970, 54758, 129825, 246255, 128, 896, 4336, 17088, 58342, 176971, 478662, 1129967, 2145722, 256, 1984, 10416

Offset: 1

Author

Peter Kagey, Apr 12 2020

Keywords

• nonn
• tabl

Comments

First row is A175962.

Examples

			Table begins:
n\k|  1   2     3      4       5        6         7          8
---+----------------------------------------------------------
  1|  1   2    10     63     454     3539     29008     246255
  2|  1   5    33    240    1871    15314    129825    1129967
  3|  2  13    98    777    6420    54758    478662    4266102
  4|  4  32   269   2295   19970   176971   1593093   14532881
  5|  8  76   702   6393   58342   536080   4965056   46345046
  6| 16 176  1768  17088  163041  1550809  14765863  140982374
  7| 32 400  4336  44280  440602  4332221  42373370  413689403
  8| 64 896 10416 111984 1159580 11771312 118190333 1179448443
For example, the T(2,2) = 5 sequences of permissible queen's moves from (1,1) to (2,2) are:
(1,1) -> (1,2) -> (2,2),
(1,1) -> (2,1) -> (1,2) -> (2,2),
(1,1) -> (2,1) -> (2,2),
(1,1) -> (2,1) -> (3,1) -> (2,2), and
(1,1) -> (3,1) -> (2,2).
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals)
• Peter Kagey, Parity bitmap for first 1024 rows and columns. (Even and odd entries and represented by black and white pixels respectively.)

Crossrefs

Cf. A175962.

Cf. A035002 (up, right), A059450 (right, up-left), A132439 (up, right, up-right), A279212 (up, right, up-left), A334016 (right, up-right, up-left).

A033877 is the analog for king moves. For both king and queen moves, A094727 is the length of the longest sequence of moves.