A238259 Area of smallest square containing n dominoes with short side lengths 1, 2, ..., n.

0, 4, 16, 36, 64, 121, 196, 289, 441, 576, 784, 1024, 1369, 1681, 2116, 2500, 3025, 3600, 4356, 5041

Offset

0,2

Comments

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

Links

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

Erich Friedman, Dominoes in Squares

Formula

a(n) = A237886(n)^2.

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
.
.  4        16           36               64
.

Crossrefs

Cf. A237986.

Sequence in context: A016742 A221285 A121317 * A063755 A166721 A085040

Adjacent sequences: A238256 A238257 A238258 * A238260 A238261 A238262

Keyword

nonn,hard,more

Author

Ivan Panchenko, Feb 21 2014

Status

approved