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

3,2

Links

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

Jon E. Schoenfield, QBasic program

Formula

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

Example

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)}.

Crossrefs

Cf. A000537, A002415, A085582, A113751.

Sequence in context: A213586 A119365 A001211 * A275112 A027178 A264314

Adjacent sequences: A122222 A122223 A122224 * A122226 A122227 A122228

Keyword

nonn

Author

Hugo Pfoertner, Sep 29 2006

Extensions

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

Status

approved