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A194476 Number of ways to arrange 4 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, 0, 6, 114, 879, 4284, 15729, 47565, 124803, 293733, 634293, 1277133, 2426424, 4389567, 7615062, 12739902, 20647962, 32540958, 50023656, 75205116, 110817861, 160356966, 228241167, 319998195, 442476645, 604086795, 815072895, 1087819551 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 4 of A194480.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..112

FORMULA

Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (5/64)*n^6 + (13/240)*n^5 + (27/128)*n^4 - (23/96)*n^3 - (13/96)*n^2 + (7/40)*n.

Empirical g.f.: x^3*(2 + 20*x + 23*x^2 - 9*x^3 - x^4) / (1 - x)^9. - Colin Barker, May 05 2018

EXAMPLE

All solutions for 3 X 3 X 3:

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

...1.1....0.1....1.1....1.1....1.0....1.1

..0.1.1..1.1.0..1.1.0..0.1.0..0.1.1..1.0.1

CROSSREFS

Cf. A194480

Sequence in context: A324669 A051228 A194132 * A059116 A121544 A274786

Adjacent sequences:  A194473 A194474 A194475 * A194477 A194478 A194479

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 26 2011

STATUS

approved

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Last modified October 17 14:47 EDT 2019. Contains 328114 sequences. (Running on oeis4.)