A376005 For integers >=2, the number of integer solutions to sqrt((n^2-c)*b^2 + c*(b+1)^2) where b and c are positive integers and c < n^2.

0, 0, 2, 2, 4, 6, 10, 8, 14, 16, 18, 22, 26, 22, 38, 36, 36, 44, 48, 42, 60, 62, 62, 64, 78, 68, 88, 90, 78, 102, 114, 92, 120, 104, 118, 134, 144, 122, 148, 156, 138, 168, 178, 142, 194, 194, 186, 192, 200, 188, 232, 230, 212, 218, 252, 224, 274, 272, 236

Offset: 2

Author

Charles L. Hohn, Sep 05 2024

Keywords

• nonn

Comments

a(n) = count(k) of A375336(n, k) for each n >= 2.

Omitting n < 2, which yield no c values that meet the rubric.

Examples

			A375336 rows n = 2 and n = 3 are empty, so a(2) = 0 and a(3) = 0.
A375336 rows n = 4 and n = 5 each contain 2 terms, so a(4) = 2 and a(5) = 2.
		

Crossrefs

Cf. A375336.

Programs

PARI

a(n)=my(d=n^2, t=n, an=0); while(t<=n^3/8, my(b=floor(sqrt(t^2/d)), r=t^2-d*b^2); if (r && r%(b*2+1)==0, an++); t++); an
for(n=2, 100, print(n, " ", a(n)))