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Easy Diagonal
In the drawing below we have a part of the Pascal’s triangle,
lines are numbered from zero (top). The left diagonal in pale
blue with only numbers equal to 1 is diagonal zero, then in
dark green (1, 2, 3, 4, 5, 6, 7) is diagonal 1, then in
pale green (1, 3, 6, 10, 15, 21) is diagonal 2 and so on.
We want to calculate the sum of the binomial coefficients on
a given diagonal. The sum on diagonal 0 is 8 (we’ll write
it S(7, 0), 7 is the number of the line where we start, 0
is the number of the diagonal). In the same way S(7, 1) is
28, S(7, 2) is 56.
Can you write a program which calculate S(n, p) where n
is the line where we start and p is the number of the diagonal?
The function will take n and p (with: n >= p >= 0) as
parameters and will return the sum.
Examples
diagonal(20, 3) => 5985
diagonal(20, 4) => 20349
Hint
When following a diagonal from top to bottom have a look at the numbers on the diagonal at its right.
References: