A333174 a(n) = Sum_{k=0..n} r_4(k^2 + 1), where r_4(k) is the number of ways of writing k as a sum of 4 squares (A000118).

8, 32, 80, 224, 368, 704, 1008, 1752, 2424, 3432, 4248, 5736, 7176, 9768, 11352, 14088, 16152, 20472, 23944, 28312, 31528, 37576, 42280, 50056, 54680, 62216, 67640, 78296, 85880, 96008, 103784, 116552, 126968, 142808, 152888, 167624, 178008, 197880, 212616, 230904

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

R. Sitaramachandrarao and P. V. Krishnaiah, On the sums Sigma_{n<=x} A(f(n)) and Sigma_{p<=x} A(f(p)), Journal of Number Theory, Vol. 23, No. 2 (1986), pp. 149-168.

Formula

a(n) ~ (40*G/Pi^2) * n^3, where G is Catalan's constant (A006752).

Example

a(0) = r_4(0^2 + 1) = r_4(1) = A000118(1) = 8.
a(1) = r_4(0^2 + 1) + r_4(1^1 + 1) = r_4(1) + r_4(2) = A000118(1) + A000118(2) = 8 + 24 = 32.

Mathematica

Accumulate @ Table[SquaresR[4, k^2 + 1], {k, 0, 100}]

Crossrefs

Partial sums of A333173.

Cf. A000118, A002522, A006752.

Sequence in context: A224543 A211633 A130809 * A372981 A018839 A008412

Adjacent sequences: A333171 A333172 A333173 * A333175 A333176 A333177

Keyword

nonn

Author

Amiram Eldar, Mar 09 2020

Status

approved