login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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,c)). 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 (list; graph; refs; listen; history; text; internal format)
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( A143714(i), i=1..n ).
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))))
/* or: */ s=0; A143715=vector(100, i, s+=A143714[i])
CROSSREFS
Cf. A143714 (first differences).
Sequence in context: A101437 A039856 A301703 * A159685 A251729 A187763
KEYWORD
easy,nonn
AUTHOR
M. F. Hasler, Aug 29 2008, Aug 30 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 25 21:07 EST 2024. Contains 370333 sequences. (Running on oeis4.)