|
|
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.
|
|
2
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
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).
|
|
CROSSREFS
|
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.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|