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A334705 Triangle read by rows: T(n,k) (1 <= k <= n) = number of ways to choose three points from an n X k grid of points which are the vertices of a triangle of nonzero area. 7
0, 0, 4, 0, 18, 76, 0, 48, 200, 516, 0, 100, 412, 1056, 2148, 0, 180, 738, 1884, 3820, 6768, 0, 294, 1200, 3052, 6176, 10922, 17600, 0, 448, 1824, 4628, 9352, 16516, 26588, 40120, 0, 648, 2632, 6668, 13456, 23740, 38192, 57588, 82608, 0, 900, 3650, 9232, 18612, 32812, 52758, 79508, 114000, 157252 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

It follows from the definitions that T(n,k) + A334704(n,k) = A334703(n,k) for 1 <= k <= n.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

Triangle begins:

0,

0, 4,

0, 18, 76,

0, 48, 200, 516,

0, 100, 412, 1056, 2148,

0, 180, 738, 1884, 3820, 6768,

0, 294, 1200, 3052, 6176, 10922, 17600,

0, 448, 1824, 4628, 9352, 16516, 26588, 40120,

0, 648, 2632, 6668, 13456, 23740, 38192, 57588, 82608,

0, 900, 3650, 9232, 18612, 32812, 52758, 79508, 114000, 157252,

0, 1210, 4900, 12380, 24940, 43934, 70608, 106364, 152456, 210234, 280988,

...

This is the lower half of a symmetric array. The full symmetric array begins:

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

0, 4, 18, 48, 100, 180, 294, 448, 648, 900, 1210, 1584, ...

0, 18, 76, 200, 412, 738, 1200, 1824, 2632, 3650, 4900, 6408, ...

0, 48, 200, 516, 1056, 1884, 3052, 4628, 6668, 9232, 12380, 16176, ...

0, 100, 412, 1056, 2148, 3820, 6176, 9352, 13456, 18612, 24940, 32568, ...

0, 180, 738, 1884, 3820, 6768, 10922, 16516, 23740, 32812, 43934, 57336, ...

0, 294, 1200, 3052, 6176, 10922, 17600, 26588, 38192, 52758, 70608, 92112, ...

0, 448, 1824, 4628, 9352, 16516, 26588, 40120, 57588, 79508, 106364, 138708, ...

0, 648, 2632, 6668, 13456, 23740, 38192, 57588, 82608, 114000, 152456, 198760, ...

0, 900, 3650, 9232, 18612, 32812, 52758, 79508, 114000, 157252, 210234, 274016 , ...

0, 1210, 4900, 12380, 24940, 43934, 70608, 106364, 152456, 210234, 280988, 366152, ...

...

CROSSREFS

This is a companion to the triangles A334703 and A334704.

Rows (or columns) 2,3,4,5 of the full array are A045991, A262402, A296367, A334707. The main diagonal is A045996.

Sequence in context: A167350 A215669 A244310 * A156457 A058348 A184946

Adjacent sequences:  A334702 A334703 A334704 * A334706 A334707 A334708

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jun 13 2020.

EXTENSIONS

Rows 6 onwards from Tom Duff (see the Duff link in A335704). - N. J. A. Sloane, Jun 19 2020

STATUS

approved

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Last modified June 26 18:18 EDT 2022. Contains 354885 sequences. (Running on oeis4.)