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Number of ways to arrange 3 nonattacking knights on the lower triangle of an n X n board.
Column 3 of A194492.
Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (17/16)*n^4 + (133/48)*n^3 + (433/24)*n^2 - (743/6)*n + 218 for n>4.
Empirical g.f.: x^2*(1 + 5*x - x^2 + 36*x^3 - 50*x^4 + 50*x^5 - 40*x^6 + 22*x^7 - 12*x^8 + 4*x^9) / (1 - x)^7. - Colin Barker, May 05 2018
Some solutions for 3X33 X 3:
Cf. A194492.
R. H. Hardin , Aug 26 2011
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editing
Number of ways to arrange 3 nonattacking knights on the lower triangle of an nXn n X n board
_R. H. Hardin (rhhardin(AT)att.net) _ Aug 26 2011
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R. H. Hardin, <a href="/A194487/b194487.txt">Table of n, a(n) for n = 1..200</a>
allocated for Ron HardinNumber of ways to arrange 3 nonattacking knights on the lower triangle of an nXn board
0, 1, 12, 62, 253, 804, 2136, 4958, 10376, 20013, 36144, 61846, 101163, 159286, 242748, 359634, 519806, 735143, 1019796, 1390458, 1866649, 2471016, 3229648, 4172406, 5333268, 6750689, 8467976, 10533678, 13001991, 15933178, 19394004
1,3
Column 3 of A194492
Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (17/16)*n^4 + (133/48)*n^3 + (433/24)*n^2 - (743/6)*n + 218 for n>4
Some solutions for 3X3
..1......0......1......1......0......0......1......0......0......0......1
..0.1....1.1....1.1....1.0....0.1....0.1....0.1....1.0....1.1....0.0....0.0
..1.0.0..1.0.0..0.0.0..1.0.0..0.1.1..1.0.1..0.0.1..1.1.0..0.1.0..1.1.1..1.0.1
allocated
nonn
R. H. Hardin (rhhardin(AT)att.net) Aug 26 2011
approved
editing
allocated for Ron Hardin
allocated
approved