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A194021
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Number of ways to arrange 4 points on an n X n X n triangular grid on an isosceles triangle so that it balances at the midpoint of its central altitude.
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1
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0, 0, 1, 8, 26, 75, 182, 387, 756, 1382, 2379, 3915, 6198, 9486, 14110, 20475, 29054, 40437, 55309, 74466, 98850, 129548, 167784, 214986, 272758, 342900, 427453, 528698, 649148, 791631, 959254, 1155429, 1383930, 1648890, 1954791, 2306565
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OFFSET
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1,4
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COMMENTS
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Column 4 of A194024.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..200
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FORMULA
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Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-4) + 5*a(n-6) - 3*a(n-7) + 3*a(n-8) - 5*a(n-9) + 2*a(n-11) + 2*a(n-13) - 3*a(n-14) + a(n-15).
Empirical g.f.: x^3*(1 + 5*x + 4*x^2 + 13*x^3 + 11*x^4 + 7*x^5 + 6*x^6 + x^7) / ((1 - x)^7*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, May 05 2018
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EXAMPLE
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Some solutions for 5 X 5 X 5:
......1..........1..........1..........1..........0..........0..........0
.....0.0........0.0........1.0........0.0........1.1........1.1........0.1
....0.1.1......1.0.0......0.0.0......1.1.0......0.0.1......0.0.0......1.1.0
...0.0.0.0....0.1.0.1....0.1.0.0....0.0.0.0....0.0.0.0....0.1.1.0....0.0.1.0
..0.1.0.0.0..0.0.0.0.0..0.0.0.1.0..0.0.0.1.0..0.1.0.0.0..0.0.0.0.0..0.0.0.0.0
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CROSSREFS
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Cf. A194024.
Sequence in context: A051669 A207101 A027004 * A245126 A278769 A173365
Adjacent sequences: A194018 A194019 A194020 * A194022 A194023 A194024
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Aug 12 2011
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STATUS
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approved
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