

A089046


Least edgelength of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem.


4



1, 2, 2, 2, 3, 3, 4, 5, 6, 8, 10, 14, 18, 24, 30, 40, 54, 71, 92, 121, 155, 210, 266, 360, 476, 642, 833, 1117, 1485, 1967, 2595, 3465, 4534, 5995
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OFFSET

1,2


COMMENTS

n <= 15 (and possibly 16) proved minimal by J. H. Conway (Conway, J. H. "Re: [mathfun] Mrs. Perkins Quilt  Orders 89, 90 improved over UPIG." mathfun mailing list. October 10, 2003.). The conjectures are best currently known values of a(n) for n > 16.  Stuart E Anderson, Apr 21 2013
Upper bounds for the next terms in the sequence (which may well be the true values) are 7907, 10293, 13505, 17785, 23239, 31035, 39571, ...  Ed Pegg Jr, Jul 06 2017


REFERENCES

H. T. Croft, K. J. Falconer, and R. K. Guy, Section C3 in Unsolved Problems in Geometry, New York: Springer, 1991.
M. Gardner, "Mrs. Perkins's Quilt and Other SquarePacking Problems," Mathematical Carnival, New York: Vintage, 1977.


LINKS



CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS

Confirmed a(30) as best known, added a(31) as best known.  Stuart E Anderson, Apr 21 2013
Using James Williams recent discoveries of 15 million simple perfect squared squares in orders 31 to 44 I was able to extend the sequence of best currently known values for optimal quilts from a(32) to a(44).  Stuart E Anderson, Apr 21 2013
Using Anderson and Milla's enumeration of order 31 and 32 perfect squared squares, improved conjectures for a(32) and a(33) were obtained  Stuart E Anderson, Sep 16 2013
a(29) corrected and further terms added by Ed Pegg Jr, Jul 06 2017


STATUS

approved



