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.

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

Author

R. H. Hardin, Aug 26 2011

Keywords

• nonn

Comments

Column 3 of A194480.

Examples

			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]
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A194480.

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