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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A018839 A008412 A014819

Adjacent sequences:  A333171 A333172 A333173 * A333175 A333176 A333177

KEYWORD

nonn

AUTHOR

Amiram Eldar, Mar 09 2020

STATUS

approved

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Last modified August 3 06:22 EDT 2021. Contains 346435 sequences. (Running on oeis4.)