Sum of 4 Consecutive Binomial Coefficients forming Square

Theorem
Consider the Diophantine equation:
 * $\dbinom n 0 + \dbinom n 1 + \dbinom n 2 + \dbinom n 3 = m^2$

where:
 * $\dbinom a b$ denotes a binomial coefficent
 * $n$ is an integer
 * $m$ is a non-negative integer.

Then $n$ has one of the following values:
 * $-1, 0, 2, 7, 15, 74, 767$

The corresponding values of $m$ are:
 * $0, 1, 2, 8, 24, 260, 8672$