A182275 Number of ways of dividing an n X n square into rectangles of integer side lengths.

1, 1, 8, 322, 70878, 84231996, 535236230270, 18100579400986674, 3250879178100782348462, 3097923464622249063718465240, 15657867573050419014814618149422562, 419678195343896524683571751908598967042082, 59647666241586874002530830848160043213559146735474

Offset

0,3

Links

Table of n, a(n) for n=0..12.

David A. Klarner and Spyros S. Magliveras, The number of tilings of a block with blocks, European Journal of Combinatorics 9 (1988), 317-330.

Joshua Smith and Helena Verrill, On dividing rectangles into rectangles

Formula

a(n) = A116694(n,n) for n > 0.

Example

For n=2 the a(2) = 8 ways to divide are:
._ _   _ _   _ _   _ _   _ _   _ _   _ _   _ _
|   | | | | |_ _| | |_| |_| | |_ _| |_|_| |_|_|
|_ _| |_|_| |_ _| |_|_| |_|_| |_|_| |_ _| |_|_|

Crossrefs

Main diagonal of A116694 and of A333476.

Cf. A034999.

Sequence in context: A308615 A041769 A209277 * A171248 A344094 A264053

Adjacent sequences: A182272 A182273 A182274 * A182276 A182277 A182278

Keyword

nonn

Author

Matthew C. Russell, Apr 23 2012

Extensions

a(11)-a(12) from Steve Butler, Mar 14 2014

Status

approved