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