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%I #19 Feb 21 2021 02:08:49
%S 1,1,2,2,5,10,4,13,33,63,8,32,98,240,454,16,76,269,777,1871,3539,32,
%T 176,702,2295,6420,15314,29008,64,400,1768,6393,19970,54758,129825,
%U 246255,128,896,4336,17088,58342,176971,478662,1129967,2145722,256,1984,10416
%N 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.
%C First row is A175962.
%H Peter Kagey, <a href="/A334017/b334017.txt">Table of n, a(n) for n = 1..10011</a> (first 141 antidiagonals)
%H Peter Kagey, <a href="/A334017/a334017.png">Parity bitmap for first 1024 rows and columns</a>. (Even and odd entries and represented by black and white pixels respectively.)
%e Table begins:
%e n\k| 1 2 3 4 5 6 7 8
%e ---+----------------------------------------------------------
%e 1| 1 2 10 63 454 3539 29008 246255
%e 2| 1 5 33 240 1871 15314 129825 1129967
%e 3| 2 13 98 777 6420 54758 478662 4266102
%e 4| 4 32 269 2295 19970 176971 1593093 14532881
%e 5| 8 76 702 6393 58342 536080 4965056 46345046
%e 6| 16 176 1768 17088 163041 1550809 14765863 140982374
%e 7| 32 400 4336 44280 440602 4332221 42373370 413689403
%e 8| 64 896 10416 111984 1159580 11771312 118190333 1179448443
%e For example, the T(2,2) = 5 sequences of permissible queen's moves from (1,1) to (2,2) are:
%e (1,1) -> (1,2) -> (2,2),
%e (1,1) -> (2,1) -> (1,2) -> (2,2),
%e (1,1) -> (2,1) -> (2,2),
%e (1,1) -> (2,1) -> (3,1) -> (2,2), and
%e (1,1) -> (3,1) -> (2,2).
%Y Cf. A175962.
%Y Cf. A035002 (up, right), A059450 (right, up-left), A132439 (up, right, up-right), A279212 (up, right, up-left), A334016 (right, up-right, up-left).
%Y A033877 is the analog for king moves. For both king and queen moves, A094727 is the length of the longest sequence of moves.
%K nonn,tabl
%O 1,3
%A _Peter Kagey_, Apr 12 2020
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