A055411 Number of points in Z^5 of norm <= n.

1, 11, 221, 1343, 5913, 16875, 42205, 89527, 176377, 313259, 532509, 853399, 1322921, 1961211, 2846933, 4005143, 5554265, 7491355, 9977557, 13065527, 16907817, 21524019, 27179909, 33921671, 42036401, 51452803, 62664773

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms 0..500 from Andrew Howroyd)

Crossrefs

Column k=5 of A302997.

Cf. A122510.

Programs

Mathematica

t[d_, n_] := t[d, n] = t[d, n - 1] + SquaresR[d, n]; t[d_, 0] = 1;
a[n_] := t[5, n^2];
a /@ Range[0, 100] (* Jean-François Alcover, Sep 27 2019, after R. J. Mathar *)

Python

# uses Python code for A046895
def A055411(n): return A046895(m:=n**2)+(sum(A046895(m-k**2) for k in range(1,n+1))<<1) # Chai Wah Wu, Jun 23 2024

Formula

a(n) = A122510(5,n^2). - R. J. Mathar, Apr 21 2010

a(n) = [x^(n^2)] theta_3(x)^5/(1 - x), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 14 2018