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A239620 Number of Euler bricks with side length a < b < c < 10^n, i.e., in a boxed parameter space with dimension 10^n. 1
0, 0, 10, 151, 1714, 17873, 180953, 1815841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

An Euler brick is a cuboid of integer side dimensions a, b, c such that the face diagonals are integers.

Because the sides of a cuboid are permutable without changing its shape, the total number of Euler bricks in the parameter space is b(n) = 6*a(n) = 0, 0, 60, 906, 10284, ...

LINKS

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Euler Brick

Index entries for sequences related to bricks

EXAMPLE

a(3) = 10, since there are the ten Euler bricks [44, 117, 240], [85, 132, 720], [88, 234, 480], [132, 351, 720], [140, 480, 693], [160, 231, 792], [176, 468, 960], [240, 252, 275], [480, 504, 550], [720, 756, 825] with longest side length < 1000.

CROSSREFS

Cf. A031173, A031174, A031175, A239618.

Sequence in context: A025750 A034325 A335800 * A253124 A178298 A251730

Adjacent sequences:  A239617 A239618 A239619 * A239621 A239622 A239623

KEYWORD

nonn,more

AUTHOR

Martin Renner, Mar 22 2014

EXTENSIONS

a(6)-a(8) from Giovanni Resta, Mar 22 2014

STATUS

approved

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Last modified October 16 06:14 EDT 2021. Contains 348040 sequences. (Running on oeis4.)