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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 17 16:32 EDT 2021. Contains 347487 sequences. (Running on oeis4.)