A356334 a(n) is the number of nonnegative integer solutions (x; y) with x <= y of x^(n+1) + y^(n+1) = (x+y)^n.

1, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset

0,2

Comments

Conjecture: a(n) = 3 except for n = 0 or n = 2. - Chai Wah Wu, Sep 21 2022

Links

Table of n, a(n) for n=0..20.

Example

For n=2, the 4 solutions are (0; 0), (0; 1), (1; 2) and (2; 2). The pairs (0; 0), (0; 1) and (2^(n-1); 2^(n-1)) exist for all n > 0.

Prog

(Python)
def A356334(n): return sum(1 for x in range((1<<n)+1) for y in range(x, (1<<n)+1) if x**(n+1)+y**(n+1)==(x+y)**n) # Chai Wah Wu, Sep 19 2022

Crossrefs

Sequence in context: A257526 A038774 A092910 * A322347 A073322 A006197

Adjacent sequences: A356331 A356332 A356333 * A356335 A356336 A356337

Keyword

nonn,more

Author

Reiner Moewald, Aug 04 2022

Extensions

a(11)-a(14) from Hugo Pfoertner, Sep 18 2022

a(15)-a(20) from Chai Wah Wu, Sep 21 2022

Status

approved