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

%I #27 Aug 13 2020 18:27:32

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

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

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

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

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

%H Erich Friedman, <a href="https://erich-friedman.github.io/packing/domino/">Dominoes in Squares</a>

%e Illustration:

%e .

%e . - - a - - - a a - - - - - - - - a a b b

%e . a a a - - - b b b b - - c c c c c c b b

%e . b b b b b b b b - - c c c c c c b b

%e . b b b b c c c c c c c c c c c c b b

%e . c c c c c c d d d d d d d d

%e . c c c c c c d d d d d d d d

%e . d d d d d d d d

%e . d d d d d d d d

%e .

%e . 2 4 6 8

%e .

%Y Cf. A211372, A238259.

%K nonn,hard,more

%O 0,2

%A _Ivan Panchenko_, Feb 15 2014

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Last modified April 19 11:31 EDT 2024. Contains 371792 sequences. (Running on oeis4.)