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
Keywords
Examples
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.
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.
Programs
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Mathematica
Accumulate @ Table[SquaresR[4, k^2 + 1], {k, 0, 100}]
Formula
a(n) ~ (40*G/Pi^2) * n^3, where G is Catalan's constant (A006752).