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A272625 Array read by antidiagonals: T(n,k) = number of ways to choose 3 distinct points from an n X k rectangular grid so that they form an acute isosceles triangle of nonzero area. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 18, 18, 0, 0, 0, 0, 30, 48, 30, 0, 0, 0, 0, 44, 84, 84, 44, 0, 0, 0, 0, 60, 128, 164, 128, 60, 0, 0, 0, 0, 78, 176, 264, 264, 176, 78, 0, 0, 0, 0, 98, 228, 374, 448, 374, 228, 98, 0, 0, 0, 0, 120, 284, 492, 650 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

A271910(n) = A272624(n) + a(n) + A272626(n).

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..3003

Chai Wah Wu, Counting the number of isosceles triangles in rectangular regular grids, arXiv:1605.00180 [math.CO], 2016.

FORMULA

T(n,k) = 3*T(n,k-1)-3*T(n,k-2)+T(n,k-3) for k > (n-1)^2+1.

CROSSREFS

Cf. A271910, A272624, A272626.

Sequence in context: A306756 A079204 A325737 * A220667 A317445 A199619

Adjacent sequences:  A272622 A272623 A272624 * A272626 A272627 A272628

KEYWORD

nonn,tabl

AUTHOR

Chai Wah Wu, May 07 2016

STATUS

approved

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Last modified July 22 16:43 EDT 2019. Contains 325225 sequences. (Running on oeis4.)