A384797 a(n) = A047800(n) - A047800(n-1).

2, 3, 4, 5, 5, 7, 7, 8, 9, 10, 10, 12, 11, 12, 14, 15, 13, 17, 15, 18, 18, 19, 17, 21, 21, 21, 22, 23, 22, 26, 23, 26, 27, 24, 28, 31, 28, 29, 29, 34, 28, 34, 32, 32, 37, 34, 35, 38, 36, 38, 38, 39, 34, 40, 42, 44, 43, 44, 42, 49, 42, 42, 46, 45, 51, 50, 46, 47, 50

Offset: 1

Author

Hugo Pfoertner, Jun 17 2025

Keywords

• nonn
• easy

Comments

This is the number of distinct positive distances of the [0,n] X [0,n] points of a lattice square from the origin that are added when the size of the square is increased from n-1 to n. Among the newly added squared distances n^2, n^2+1^2, n^2+2^2, ..., n^2+n^2, some may already have occurred in smaller lattice point squares and are therefore not counted.

Examples

			a(1) = 2: Newly added squared distances are 1 and 2.
a(5) = 5: The squared distance 25=5^2+0^2 already occurs as 4^2+3^2.
a(13) = 11: There are 3 already represented squared distances, 13^2+0^2=12^2+5^2, 13^2+1^2=11^2+7^2, 13^2+4^2=11^2+8^2.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A047800, A160663, A384798, A384799.

Programs

Python

def A384797(n):
    s = set(i**2+j**2 for i in range(n) for j in range(i+1))
    return n+1-sum(1 for i in range(n+1) if n**2+i**2 in s) # Chai Wah Wu, Jul 07 2025