Although the answer can be simply taken from Pascal's Triangle as

C(n+1,2)+2C(n+1,3)

the challenge of the exercise was to deduce the same answer by setting up a particular configuration of dots.To make a long story short... that's how I spent my entire free Saturday. By not finding the answer that is. I did this ( Sunday ) morning though with great relief. I was close right away but I -sort of- forgot to finish it correctly, instead I kept searching for other, better dot configurations. In the rush of having solved another 'difficult' exercise I remembered an article with the title 'Addicted To Knowledge' which explains the feeling I had.

Aigner says in the preface: 'It is commonplace to stress the importance of exercises. To learn enumerative combinatorics one simply must do as many exercises as possible.' An exercise is only an exercise if it was a challenging exercise, I would like to add. And harder means deeper in the context of exercises.

Hint to the answer: find a dot-configuration for the sum of 1,2,3,...,n first.

Was the idea to stack the dots in 3 dimensions as a pyramid?

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