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

1,3

Comments

Column 3 of A194480.

Links

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

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

Adjacent sequences: A194472 A194473 A194474 * A194476 A194477 A194478

Keyword

nonn

Author

R. H. Hardin, Aug 26 2011

Status

approved