A269133 Number of ways to place m nonattacking queens on an m X n board, 1 <= m <= n (triangular array).

1, 2, 0, 3, 2, 0, 4, 6, 4, 2, 5, 12, 14, 12, 10, 6, 20, 36, 46, 40, 4, 7, 30, 76, 140, 164, 94, 40, 8, 42, 140, 344, 568, 550, 312, 92, 9, 56, 234, 732, 1614, 2292, 2038, 1066, 352, 10, 72, 364, 1400, 3916, 7552, 9632, 7828, 4040, 724, 11, 90, 536, 2468, 8492, 21362, 37248, 44148, 34774, 15116, 2680, 12, 110, 756, 4080, 16852, 52856, 120104, 195270, 222720, 160964, 68264, 14200

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Math StackExchange, State space for eight queen problem

Marko Riedel, Perl program to compute triangular array of nonattacking queens configurations

Example

The triangular array begins:
   n\m  1   2   3    4     5     6      7      8      9     10    11    12
   1    1
   2    2   0
   3    3   2   0
   4    4   6   4    2
   5    5  12  14   12    10
   6    6  20  36   46    40     4
   7    7  30  76  140   164    94     40
   8    8  42 140  344   568   550    312     92
   9    9  56 234  732  1614  2292   2038   1066    352
  10   10  72 364 1400  3916  7552   9632   7828   4040    724
  11   11  90 536 2468  8492 21362  37248  44148  34774  15116  2680
  12   12 110 756 4080 16852 52856 120104 195270 222720 160964 68264 14200
...

Prog

(PARI) {A269133(m, n, B=[], t=if(#B, setminus(n, Set(concat(B+t=[-#B..-1], B-t))), n=[1..n]))= if(#B < m-1, vecsum([A269133(m, setminus(n, [t]), concat(B, t)) | t<-t]), #t)} \\ M. F. Hasler, Jan 11 2022

Crossrefs

Cf. A000170 (m=n), A002562, A065256, A348129.

Cf. A000027 (m=1), A002378 (m=2), A061989 (m=3), A061990 (m=4), A061991 (m=5), A061992 (m=6), A061993 (m=7), A172449 (m=8).

Cf. A036464 (2Q), A047659 (3Q), A061994 (4Q), A108792 (5Q), A176186 (6Q).

Cf. A006717, A051906, A319284 (backtrack trees).

Sequence in context: A342238 A154559 A342239 * A143324 A287416 A097418

Adjacent sequences: A269130 A269131 A269132 * A269134 A269135 A269136

Keyword

nonn,tabl

Author

Marko Riedel, Feb 19 2016

Status

approved