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URL: https://oeis.org/A055411

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A055411
Number of points in Z^5 of norm <= n.
7
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
0,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms 0..500 from Andrew Howroyd)
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
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 *)
PROG
(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
CROSSREFS
Column k=5 of A302997.
Cf. A122510.
Sequence in context: A204236 A035012 A179339 * A341491 A064093 A087402
KEYWORD
nonn
STATUS
approved