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Problem of the Day #277: The Holiday Present December 21, 2011

Posted by Saketh in : potd , trackback

Albert is preparing holiday gifts for his friends. He knows that Sreenath has trolled a lot this past year, so he will be giving him $1$x$1$x$2$ bricks of coal. The coal will be packed in a $2$x$2$x$n$ box.

Suppose that $a_n$ is the number of distinct ways the coal can be packed for a given value of $n$. For which values of $n$ is $a_n$ a perfect square?

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