

A089047


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


6



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
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OFFSET

1,4


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

Table of n, a(n) for n=1..33.
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], 20132014.


CROSSREFS

Cf. A005670, A014529, A018835, A089046, A211302, A290821.
Sequence in context: A173090 A032277 A205579 * A133498 A282949 A292200
Adjacent sequences: A089044 A089045 A089046 * A089048 A089049 A089050


KEYWORD

nonn,hard,more


AUTHOR

R. K. Guy, Dec 03 2003


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


STATUS

approved



