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A319284 The profiles of the backtrack tree for the n queens problem, triangle read by rows. 6
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, 30, 76, 140, 164, 94, 40, 1, 8, 42, 140, 344, 568, 550, 312, 92, 1, 9, 56, 234, 732, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
The profile (p_0, p_1, ..., p_n) is the number of nodes at each level of the tree.
REFERENCES
D. E. Knuth, The Art of Computer Programming, Volume 4, Pre-fascicle 5B, Introduction to Backtracking, 7.2.2. Backtrack programming. 2018.
LINKS
Candida Bowtell and Peter Keevash, The n-queens problem, arXiv:2109.08083 [math.CO] 2021.
V. Kotesovec, Ways of placing non-attacking queens and kings..., part of "Between chessboard and computer", 1996, pp. 204 - 206.
Michael Simkin, The number of n-queens configurations, arXiv:2107.13460 [math.CO] 2021.
Wikipedia, Backtracking
EXAMPLE
[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, 30, 76, 140, 164, 94, 40]
[1, 8, 42, 140, 344, 568, 550, 312, 92]
[1, 9, 56, 234, 732, 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]
[1, 12, 110, 756, 4080, 16852, 52856, 120104, 195270, 222720, 160964, 68264, 14200]
PROG
(Julia) See the link section.
CROSSREFS
Cf. A000170 (T(n,n)), A319283 (row sums), A319288 (indices of the row maxima).
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).
Sequence in context: A216235 A306914 A317023 * A338526 A182703 A354006
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 16 2018
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)