MathDB

The triangular domino is a game that uses the tokens shown below, with equilateral triangle shape with side

1

. The idea of the game is to construct an equilateral triangle with side

n

, no gaps, following the rules of the domino or classic.

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Show that the sum

S

of the values corresponding to the edges that are part of the sides of the greater triangle, it depends only on n, and not on the way in which the tokens are paired.

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For each value of

n

, calculate

S

. https://cdn.artofproblemsolving.com/attachments/e/9/898664fac380725a7398dfe470298a90b8c69b.png

4

Problems(1)