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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

First row is A175962.

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.)

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. 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.

Sequence in context: A309867 A304584 A193899 * A208567 A273968 A273964

Adjacent sequences:  A334014 A334015 A334016 * A334018 A334019 A334020

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Apr 12 2020

STATUS

approved

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Last modified June 26 14:05 EDT 2022. Contains 354884 sequences. (Running on oeis4.)