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A194131 Number of ways to arrange 3 indistinguishable points on an n X n X n triangular grid so that no three points are collinear at any angle. 2
0, 0, 1, 17, 105, 407, 1216, 3036, 6696, 13428, 25005, 43861, 73277, 117471, 181880, 273268, 399960, 572076, 801825, 1103625, 1494541, 1994387, 2626152, 3416300, 4395148, 5596992, 7060737, 8830137, 10954197, 13487527, 16490972, 20031672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Column 3 of A194136.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..500, Mar 20 2016 [First 196 terms from R. H. Hardin]

StackExchange, Number of possible triangles in a given triangle.

FORMULA

a(n) = ((n^2+n+2)/2) * binomial(n+2,4) - (3/2) * Sum_{k=2..n} (n-k+1) * (n-k+2) * Sum_{m=2..k} gcd(k-1,m-1). - David Bevan, Jan 01 2012

EXAMPLE

Some solutions for 3X3X3

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

...1.1....1.0....0.1....1.0....0.0....0.0....1.1....1.1....0.1....0.1....0.1

..0.0.1..0.0.1..1.0.0..1.1.0..0.1.1..1.0.1..0.0.0..0.1.0..1.1.0..0.1.0..1.0.1

CROSSREFS

Cf. A194136.

Sequence in context: A160219 A242316 A095785 * A194475 A164745 A221938

Adjacent sequences:  A194128 A194129 A194130 * A194132 A194133 A194134

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 17 2011

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)