A089047 Edge length of largest square dissectable into up to n squares in Mrs. Perkins's quilt problem.

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 13, 17, 23, 29, 41, 53, 70, 91, 126, 158, 216, 276, 386, 488, 675, 866, 1179, 1544, 2136, 2739, 3755, 4988, 6443

Offset: 1

Author

R. K. Guy, Dec 03 2003

Keywords

• nonn
• hard
• more

Comments

An inverse to A005670.

More precisely, a(n) = greatest k such that A005670(k) <= n. - Peter Munn, Mar 13 2018

It is not clear which terms have been proved to be correct and which are just conjectures. - Geoffrey H. Morley, Sep 07 2012; N. J. A. Sloane, Jul 06 2017

Terms up to and including a(18) have been proved correct by Ed Wynn (2013). - Stuart E Anderson, Sep 16 2013

A089046 and A089047 are almost certainly correct up to 5000. - Ed Pegg Jr, Jul 06 2017

Deleted terms above 5000. - N. J. A. Sloane, Jul 06 2017

Further best known terms are 8568, 11357, 14877, 19594, 26697, 34632. - Ed Pegg Jr, Jul 06 2017

A290821 is the equivalent sequence for equilateral triangles. - Peter Munn, Mar 06 2018

Links

• Ed Pegg, Jr., Mrs. Perkins's Quilts
• Ed Pegg Jr. and Richard K. Guy, Mrs. Perkins's Quilts (Wolfram Demonstrations Project)
• Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, arXiv:1308.5420 [math.CO], 2013-2014.

Crossrefs

Cf. A005670, A014529, A018835, A089046, A211302, A290821.

Extensions

More terms from Ed Pegg Jr, Dec 03 2003

Corrected and extended by Ed Pegg Jr, Apr 18 2010

Duplicate a(6) deleted and a(22)-a(26) revised (from Ed Pegg Jr, Jun 15 2010) by Geoffrey H. Morley, Sep 07 2012

Conjectured terms have been extended up to a(44), based on simple squared square enumeration, by Duijvestijn, Skinner, Anderson, Pegg, Johnson, Milla and Williams. - Stuart E Anderson, Sep 16 2013

a(33) and further terms added by Ed Pegg Jr, Jul 06 2017

Name edited by Peter Munn, Mar 14 2018