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A319284 The profiles of the backtrack tree for the n queens problem, triangle read by rows.

%I A319284 #27 Mar 31 2024 12:04:57
%S A319284 1,1,1,1,2,0,1,3,2,0,1,4,6,4,2,1,5,12,14,12,10,1,6,20,36,46,40,4,1,7,
%T A319284 30,76,140,164,94,40,1,8,42,140,344,568,550,312,92,1,9,56,234,732,
%U A319284 1614,2292,2038,1066,352,1,10,72,364,1400,3916,7552,9632,7828,4040,724,1,11,90,536,2468,8492,21362,37248,44148,34774,15116,2680
%N A319284 The profiles of the backtrack tree for the n queens problem, triangle read by rows.
%C A319284 The profile (p_0, p_1, ..., p_n) is the number of nodes at each level of the tree.
%D A319284 D. E. Knuth, The Art of Computer Programming, Volume 4, Pre-fascicle 5B, Introduction to Backtracking, 7.2.2. Backtrack programming. 2018.
%H A319284 Peter Luschny, <a href="/A319284/b319284.txt">Rows n = 0..19, flattened</a>
%H A319284 Candida Bowtell and Peter Keevash, <a href="https://arxiv.org/abs/2109.08083">The n-queens problem</a>, arXiv:2109.08083 [math.CO] 2021.
%H A319284 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Ways of placing non-attacking queens and kings...</a>, part of "Between chessboard and computer", 1996, pp. 204 - 206.
%H A319284 Peter Luschny, <a href="/A319284/a319284.jl.txt">Julia implementation of the n queens problem with profiles</a>
%H A319284 Michael Simkin, <a href="https://arxiv.org/abs/2107.13460">The number of n-queens configurations</a>, arXiv:2107.13460 [math.CO] 2021.
%H A319284 Wikipedia, <a href="https://en.wikipedia.org/wiki/Backtracking">Backtracking</a>
%H A319284 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight queens puzzle</a>
%e A319284 [1]
%e A319284 [1,  1]
%e A319284 [1,  2,  0]
%e A319284 [1,  3,  2,    0]
%e A319284 [1,  4,  6,    4,    2]
%e A319284 [1,  5,  12,  14,   12,    10]
%e A319284 [1,  6,  20,  36,   46,    40,     4]
%e A319284 [1,  7,  30,  76,  140,   164,    94,     40]
%e A319284 [1,  8,  42, 140,  344,   568,   550,    312,     92]
%e A319284 [1,  9,  56, 234,  732,  1614,  2292,   2038,   1066,    352]
%e A319284 [1, 10,  72, 364, 1400,  3916,  7552,   9632,   7828,   4040,    724]
%e A319284 [1, 11,  90, 536, 2468,  8492, 21362,  37248,  44148,  34774,  15116,  2680]
%e A319284 [1, 12, 110, 756, 4080, 16852, 52856, 120104, 195270, 222720, 160964, 68264, 14200]
%o A319284 (Julia) # See the link section.
%Y A319284 Cf. A000170 (T(n,n)), A319283 (row sums), A319288 (indices of the row maxima).
%Y A319284 Cf. A000012 (col. 0), A000027 (col. 1), A002378 (col. 2), A061989 and A079908 (col. 3), A061990 (col. 4), A061991 (col. 5), A061992 (col. 6), A061993 (col. 7), A172449 (col. 8).
%K A319284 nonn,tabl
%O A319284 0,5
%A A319284 _Peter Luschny_, Sep 16 2018