A063014 Number of solutions to n^2 = b^2 + c^2 (with c >= b >= 0).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 5, 1, 1, 2, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 1, 5, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 2

Offset: 0

Author

Henry Bottomley, Jul 26 2001

Keywords

• nonn

Examples

			a(0)=1 since 0^2 = 0^2 + 0^2;
a(5)=2 since 5^2 = 0^2 + 5^2 = 3^2 + 4^2;
a(25)=3 since 25^2 = 0^2 + 25^2 = 7^2 + 24^2 = 15^2 + 20^2.
		

Links

• Felix Huber, Table of n, a(n) for n = 0..10000
• Michael Gilleland, Some Self-Similar Integer Sequences

Crossrefs

Cf. A000161, A046080.

Column k=2 of A255212.

Programs

Maple

with(NumberTheory):
A063014 := n -> nops(SumOfSquares(n^2));
seq(A063014(n), n = 0 .. 100); # Felix Huber, Jun 01 2024

Formula

a(0) = 1; a(n) = A046080(n) + 1 for n > 0. [amended by Georg Fischer, Jan 25 2020]

a(n) = A000161(n^2). - Christian Krause, Dec 08 2022