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A194482
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Number of ways to arrange 5 indistinguishable points on an n X n X n triangular grid so that no four points are in the same row or diagonal.
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1
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0, 0, 6, 234, 2817, 19362, 94584, 365904, 1193283, 3413619, 8800704, 20845968, 46017972, 95710797, 189154056, 357631176, 650438802, 1143119610, 1948614426, 3232108278, 5230489803, 8277505236, 12835867968, 19537783320, 29235566685
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (1/384)*n^8 - (59/1920)*n^7 + (281/3840)*n^6 + (149/3840)*n^5 - (5/24)*n^4 + (29/320)*n^3 + (11/80)*n^2 - (1/10)*n.
Empirical g.f.: 3*x^3*(2 + 56*x + 191*x^2 + 85*x^3 - 31*x^4 + 11*x^5 + x^6) / (1 - x)^11. - Colin Barker, May 05 2018
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EXAMPLE
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Some solutions for 4 X 4 X 4:
.....1........1........0........1........0........0........0........0
....1.1......1.0......1.1......0.0......0.1......1.1......1.0......1.1
...0.1.1....0.1.0....0.1.0....1.0.1....0.1.0....1.0.1....1.0.0....1.0.0
..0.0.0.0..0.1.0.1..0.1.1.0..1.1.0.0..0.1.1.1..0.1.0.0..1.1.0.1..1.1.0.0
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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