A237886 Side length of smallest square containing n dominoes with short side lengths 1, 2, ..., n.

0, 2, 4, 6, 8, 11, 14, 17, 21, 24, 28, 32, 37, 41, 46, 50, 55, 60, 66, 71

Offset

0,2

Comments

A domino with short side length k has dimensions k X 2k.

Terms a(5) to a(13) were found by Erich Friedman in 1998, a(14) to a(19) by Erich Friedman in January 2004.

a(n) >= ceiling(sqrt(n*(n + 1)*(2n + 1)/3)).

Links

Table of n, a(n) for n=0..19.

Erich Friedman, Dominoes in Squares

Example

Illustration:
.
. - -    a - - -    a a - - - -    - - - - a a b b
. a a    a - - -    b b b b - -    c c c c c c b b
.        b b b b    b b b b - -    c c c c c c b b
.        b b b b    c c c c c c    c c c c c c b b
.                   c c c c c c    d d d d d d d d
.                   c c c c c c    d d d d d d d d
.                                  d d d d d d d d
.                                  d d d d d d d d
.
.  2        4            6                8
.

Crossrefs

Cf. A211372, A238259.

Sequence in context: A092777 A186380 A006463 * A212555 A328787 A339573

Adjacent sequences: A237883 A237884 A237885 * A237887 A237888 A237889

Keyword

nonn,hard,more

Author

Ivan Panchenko, Feb 15 2014

Status

approved