A309395 Number of integer-sided triangles with sides a,b,c, max(a,b) < c, a + c = n that are right triangles.
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 3, 4, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 6, 1, 4
Offset: 1
Keywords
Examples
n | (a,b,c) -----+----------------------------------------- 8 | [ 3, 4, 5] 9 | [ 4, 3, 5] 16 | [ 6, 8, 10] 18 | [ 5, 12, 13], [ 8, 6, 10] 24 | [ 9, 12, 15] 25 | [ 8, 15, 17], [12, 5, 13] 27 | [12, 9, 15] 32 | [ 7, 24, 25], [12, 16, 20], [15, 8, 17] 36 | [10, 24, 26], [16, 12, 20]
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..1000
Programs
-
PARI
{a(n) = sum(k=n\2+1, n-1, issquare(k^2-(n-k)^2))}