A122225 (1/4)*number of nonsquare rectangles with corners on an n X n grid of points.

1, 6, 20, 52, 111, 214, 376, 620, 967, 1452, 2096, 2952, 4047, 5422, 7128, 9236, 11773, 14834, 18450, 22704, 27675, 33460, 40090, 47708, 56383, 66214, 77276, 89748, 103647, 119206, 136476, 155592, 176681, 199858, 225224, 253104, 283555, 316692

Offset: 3

Author

Hugo Pfoertner, Sep 29 2006

Keywords

• nonn

Examples

			a(3)=1 because there are 4 rectangles that can be formed on the square grid [0,1,2] X [0,1,2]: {(0 0),(0 1),(2 0),(2 1)}, {(0 0),(0 2),(1 0),(1 2)}, {(0 1),(0 2),(2 1),(2 2)}, {(1 0),(1 2),(2 0),(2 2)}.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 3..500
• Jon E. Schoenfield, QBasic program

Crossrefs

Cf. A000537, A002415, A085582, A113751.

Formula

a(n) = (A085582(n) - A002415(n))/4.

Extensions

Corrected and extended by Jon E. Schoenfield, Oct 08 2006