

A195984


The size of the smallest boundary square in simple perfect squared rectangles of order n.


0



8, 13, 22, 18, 14, 13, 11, 9, 6, 9, 7, 7, 8, 6, 8, 7
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OFFSET

9,1


COMMENTS

Ian Gambini showed in his thesis that the minimum value for a(n) is 5. Brian Trial found 3 simple perfect squared rectangles (SPSRs) of order 28 with boundary squares of size 5 in September 2011. An unsolved problem is to find the lowest order SPSR with a '5 on the side'.
Added a(22) = 6 (Stuart Anderson), Brian Trial has found a(28) = 5. This gives an upper bound of 28, in addition to the lower bound of 23, to the problem of finding the lowest order SPSR with a square of size 5 on the boundary.  Stuart E Anderson, Sep 29 2011
Found a(23) = 8, the lower bound is now order 24.  Stuart E Anderson, Nov 30 2012
Found a(24) = 7, the lower bound is now order 25.  Stuart E Anderson, Dec 07 2012


REFERENCES

Gambini, Ian. Thesis; 'Quant aux carrés carrelés' L’Universite de la Mediterranee AixMarseille II 1999


LINKS

Table of n, a(n) for n=9..24.
Stuart E. Anderson, Simple Perfects by Boundary Rules and Conditions
Stuart Anderson, 'Special' Perfect Squared Squares", accessed 2014.  N. J. A. Sloane, Mar 30 2014


CROSSREFS

Cf. A002839.
Sequence in context: A273980 A101642 A269354 * A019535 A229446 A205704
Adjacent sequences: A195981 A195982 A195983 * A195985 A195986 A195987


KEYWORD

nonn


AUTHOR

Stuart E Anderson, Sep 26 2011


EXTENSIONS

Added a(23) = 8, Stuart E Anderson, Nov 30 2012
Added a(24) = 7, Stuart E Anderson, Dec 07 2012


STATUS

approved



