A228953 The largest possible element size for each perfect squared square order, otherwise 0 if perfect squared squares do not exist in that order.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 97, 134, 200, 343, 440, 590, 797, 1045, 1435, 1855, 2505, 3296, 4528, 5751, 7739, 10361

Offset

1,21

Comments

A squared rectangle is a rectangle dissected into a finite number, two or more, of squares, called the elements of the dissection. If no two of these squares have the same size the squared rectangle is called perfect, otherwise it is imperfect. The order of a squared rectangle is the number of constituent squares. The case in which the squared rectangle is itself a square is called a squared square. The dissection is simple if it contains no smaller squared rectangle, otherwise it is compound. Every perfect square with the largest known element for each order up to 37 is simple.

Links

Table of n, a(n) for n=1..37.

S. E. Anderson, Perfect Squared Rectangles and Squared Squares

Stuart Anderson, 'Special' Perfect Squared Squares", accessed 2014. - N. J. A. Sloane, Mar 30 2014

Eric Weisstein's World of Mathematics, Perfect Square Dissection

Jim Williams, Jim Williams' squared square research.

Crossrefs

Cf. A217149, A129947, A006983.

Sequence in context: A349208 A224551 A262149 * A335480 A375137 A255585

Adjacent sequences: A228950 A228951 A228952 * A228954 A228955 A228956

Keyword

nonn

Author

Stuart E Anderson, Oct 06 2013

Extensions

More terms, a(33) to a(37), extracted from Jim Williams' discoveries, added by Stuart E Anderson, Nov 06 2020

Status

approved