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

%I A269133 #23 Jan 11 2022 21:56:40
%S A269133 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,
%T A269133 40,8,42,140,344,568,550,312,92,9,56,234,732,1614,2292,2038,1066,352,
%U A269133 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
%N A269133 Number of ways to place m nonattacking queens on an m X n board, 1 <= m <= n (triangular array).
%H A269133 Math StackExchange, <a href="http://math.stackexchange.com/questions/1657276/">State space for eight queen problem</a>
%H A269133 Marko Riedel, <a href="/A269133/a269133.pl.txt">Perl program to compute triangular array of nonattacking queens configurations</a>
%e A269133 The triangular array begins:
%e A269133    n\m  1   2   3    4     5     6      7      8      9     10    11    12
%e A269133    1    1
%e A269133    2    2   0
%e A269133    3    3   2   0
%e A269133    4    4   6   4    2
%e A269133    5    5  12  14   12    10
%e A269133    6    6  20  36   46    40     4
%e A269133    7    7  30  76  140   164    94     40
%e A269133    8    8  42 140  344   568   550    312     92
%e A269133    9    9  56 234  732  1614  2292   2038   1066    352
%e A269133   10   10  72 364 1400  3916  7552   9632   7828   4040    724
%e A269133   11   11  90 536 2468  8492 21362  37248  44148  34774  15116  2680
%e A269133   12   12 110 756 4080 16852 52856 120104 195270 222720 160964 68264 14200
%e A269133 ...
%o A269133 (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
%Y A269133 Cf. A000170 (m=n), A002562, A065256, A348129.
%Y A269133 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).
%Y A269133 Cf. A036464 (2Q), A047659 (3Q), A061994 (4Q), A108792 (5Q), A176186 (6Q).
%Y A269133 Cf. A006717, A051906, A319284 (backtrack trees).
%K A269133 nonn,tabl
%O A269133 1,2
%A A269133 _Marko Riedel_, Feb 19 2016