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A194481 Number of ways to arrange 4 indistinguishable points on an n X n X n triangular grid so that no four points are in the same row or diagonal. 1
0, 0, 15, 207, 1347, 5922, 20307, 58527, 148239, 339669, 718344, 1422564, 2666664, 4771221, 8201466, 13615266, 21922146, 34354926, 52555653, 78677613, 115505313, 166594428, 236433813, 330631785, 456128985, 621440235, 836927910, 1115109450 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 4 of A194485.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..84

FORMULA

Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (1/64)*n^6 - (13/120)*n^5 + (19/128)*n^4 + (7/96)*n^3 - (13/96)*n^2 + (1/40)*n.

Empirical g.f.: x^3*(5 + 24*x + 8*x^2 - 3*x^3 + x^4) / (1 - x)^9. - Colin Barker, May 05 2018

EXAMPLE

Some solutions for 4 X 4 X 4:

.....0........0........1........0........0........0........0........0

....1.0......0.0......0.0......0.0......1.0......1.0......0.1......1.0

...1.1.1....1.0.1....1.0.1....1.0.1....1.0.0....1.0.0....0.0.1....1.0.1

..0.0.0.0..1.1.0.0..0.0.1.0..0.0.1.1..0.1.0.1..0.0.1.1..1.0.0.1..0.0.0.1

CROSSREFS

Cf. A194485.

Sequence in context: A061637 A231546 A063906 * A078265 A089138 A271333

Adjacent sequences:  A194478 A194479 A194480 * A194482 A194483 A194484

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 26 2011

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)