The nth term of sequence of triangle numbers is given by, tn = (1/2)n(n+1), so the first ten triangle numbers are:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
By converting each letter in a word corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.
Using words array of n-length, find the number of triangle words. Begin by entering a number.