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A194477 Number of ways to arrange 5 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, 0, 39, 909, 8568, 50526, 221508, 789453, 2412333, 6542316, 16127397, 36762726, 78495417, 158548572, 305303544, 563965038, 1004432454, 1732013856, 2901747051, 4737236427, 7555075374, 11796103242, 18064943820, 27179490195, 40232239515 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Column 5 of A194480.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..47

FORMULA

Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (7/384)*n^8 + (37/1920)*n^7 + (737/3840)*n^6 - (2347/3840)*n^5 + (101/192)*n^4 + (93/320)*n^3 - (7/10)*n^2 + (3/10)*n.

Empirical g.f.: 3*x^4*(13 + 160*x + 238*x^2 - 54*x^3 - 51*x^4 + 9*x^5) / (1 - x)^11. - Colin Barker, May 05 2018

EXAMPLE

Some solutions for 4 X 4 X 4:

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

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

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

..0.0.1.1..0.1.1.0..0.1.1.0..1.1.0.0..0.1.0.1..0.1.1.0..0.1.0.1..1.1.0.0

CROSSREFS

Cf. A194480.

Sequence in context: A264458 A004330 A069418 * A016091 A028227 A028219

Adjacent sequences:  A194474 A194475 A194476 * A194478 A194479 A194480

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 26 2011

STATUS

approved

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Last modified October 17 07:39 EDT 2021. Contains 348048 sequences. (Running on oeis4.)