

A085582


The number of rectangles (orthogonal or not) with corners on an n X n grid of points.


5



0, 1, 10, 44, 130, 313, 640, 1192, 2044, 3305, 5078, 7524, 10750, 14993, 20388, 27128, 35448, 45665, 57922, 72636, 89970, 110297, 133976, 161440, 192860, 228857, 269758, 316012, 367974, 426417, 491468, 564120, 644640, 733633, 831674, 939292
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..36.


FORMULA

a(n)=A000537(n)+A113751(n).  T. D. Noe, Nov 09 2005


EXAMPLE

a(3)=10 because on the 3 X 3 grid there are four 1 X 1 rectangles, two 1 X 2s, two 2 X 1's, one 2 X 2 and one 45degree rectangle, sqrt(2) X sqrt(2).


CROSSREFS

Cf. A000537, A002415, A113751 (diagonal rectangles on an n X n grid).
Sequence in context: A256050 A257052 A008532 * A058310 A005720 A060326
Adjacent sequences: A085579 A085580 A085581 * A085583 A085584 A085585


KEYWORD

nonn


AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 06 2003


EXTENSIONS

Edited by Don Reble, Nov 05 2005


STATUS

approved



