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A194475
Number of ways to arrange 3 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
1
0, 1, 17, 105, 410, 1225, 3066, 6762, 13560, 25245, 44275, 73931, 118482, 183365, 275380, 402900, 576096, 807177, 1110645, 1503565, 2005850, 2640561, 3434222, 4417150, 5623800, 7093125, 8868951, 11000367, 13542130, 16555085, 20106600
OFFSET
1,3
COMMENTS
Column 3 of A194480.
LINKS
FORMULA
Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (3/16)*n^4 + (1/48)*n^3 + (1/6)*n^2 - (1/12)*n.
Empirical g.f.: x^2*(1 + 10*x + 7*x^2 - 3*x^3) / (1 - x)^7. - Colin Barker, May 05 2018
EXAMPLE
The 17 solutions for 3 X 3 X 3:
.
1 1 1 1 1 1
1 1 1 0 1 0 0 1 0 1 0 0
0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0
1 1 0 0 0
0 0 0 0 1 1 1 1 1 1
1 0 1 0 1 1 1 0 0 0 1 0 0 0 1
0 0 0 0 0 0
1 0 1 0 1 0 0 1 0 1 0 1
1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1
[edited by Jon E. Schoenfield, May 05 2018]
CROSSREFS
Cf. A194480.
Sequence in context: A329386 A095785 A194131 * A164745 A221938 A121823
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 26 2011
STATUS
approved