VOOZH about

URL: https://oeis.org/A143715

⇱ A143715 - OEIS

login
A143715
Number of subsets {a,b,c} of {1,...,n} such that (a+b)^2+c^2 is a square (where c = max(a,b)) and a <= b.
2
0, 0, 2, 3, 3, 6, 6, 10, 14, 14, 14, 25, 25, 25, 35, 43, 43, 50, 50, 67, 85, 85, 85, 113, 113, 113, 123, 139, 139, 158, 158, 173, 191, 191, 197, 230, 230, 230, 244, 286, 286, 321, 321, 337, 379, 379, 379, 456, 456, 456, 474, 493, 493, 512, 536, 589, 609, 609, 609
OFFSET
1,3
COMMENTS
Also: Number of cuboids of side lengths not exceeding n such that the shortest path over the surface from one vertex to the opposite one is integral (cf. link to Project Euler).
Also: partial sums of A143714, i.e., number of triples (a,b,c), 1 <= a <= b <= c <= n, such that (a+b)^2+c^2 is a square.
LINKS
Project Euler, Problem 86: Cuboid Route, (2005).
FORMULA
a(n) = Sum_{i=1..n} A143714(i).
EXAMPLE
We have a(4) = a(5) = 3, corresponding to the cuboids of size 3 X 3 X 1, 3 X 2 X 2 and 4 X 2 X 1, i.e. to A143714(3)=2 and A143714(4)=1. No other cuboids with side lengths not exceeding 5 have the property that (a+b)^2+c^2 is a square. See A143714 for more details.
PROG
(PARI) A143715(M)=sum(a=1, M, sum(b=a, M, sum(c=b, M, issquare((a+b)^2+c^2))))
(PARI) s=0; A143715=vector(100, i, s+=A143714[i])
CROSSREFS
Cf. A004431, A143714 (first differences).
Sequence in context: A101437 A039856 A301703 * A159685 A370804 A251729
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Aug 29 2008, Aug 30 2008
STATUS
approved