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A220167 Number of simple squared rectangles of order n up to symmetry. 0
3, 6, 22, 76, 247, 848, 2892, 9969, 34455, 119894, 420582, 1482874, 5254954, 18714432, 66969859, 240739417 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A squared rectangle (which may be a square) is a rectangle dissected into a finite number, two or more, of integer sized squares. If no two of these squares have the same size the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle. The order of a squared rectangle is the number of constituent squares.  This sequence counts simple perfect squared rectangles and simple imperfect squared rectangles.

REFERENCES

See A006983 and A217156 for references and links.

LINKS

Table of n, a(n) for n=1..16.

S. E. Anderson, Simple Perfect Squared Rectangles [Nonsquare rectangles only]

S. E. Anderson, Simple Perfect Squared Squares

S. E. Anderson, Simple Imperfect Squared Rectangles [Nonsquare rectangles only]

S. E. Anderson, Simple Imperfect Squared Squares

FORMULA

a(n) = A002839(n) + A002881(n).

a(n) = A006983(n) + A002962(n) + A220165(n) + A219766(n).

a(n) = ((n^(-5/2))*(4^n))/(2^5*sqrt(pi)), from 'A Census of Planar Maps', William Tutte gave an asymptotic formula for the number of perfect squared rectangles where n is the number of elements in the dissection (the order).

CROSSREFS

Cf. A002839, A002881, A006983, A002962, A220165, A219766.

Sequence in context: A208939 A209067 A220166 * A243336 A029848 A117850

Adjacent sequences:  A220164 A220165 A220166 * A220168 A220169 A220170

KEYWORD

nonn,hard

AUTHOR

Stuart E Anderson, Dec 06 2012

EXTENSIONS

a(9)-a(24) from Stuart E Anderson Dec 07 2012

STATUS

approved

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Last modified December 13 01:33 EST 2017. Contains 295954 sequences.