OFFSET
1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
Lim_{n -> oo} a(n)/(n^2) -> Pi/8.
a(n) = 2 * Sum_{k=1..floor(n/2)} floor(sqrt((n/2)^2 - k^2)).
a(n) = 2 * A136483(n).
a(n) = (1/2) * A136485(n).
a(n) = [x^(n^2)] (theta_3(x^4) - 1)^2 / (2 * (1 - x)). - Ilya Gutkovskiy, Nov 24 2021
EXAMPLE
a(3) = 2 because a circle centered at the origin and of radius 3/2 encloses (-1,1) and (1,1) in the upper half plane.
MATHEMATICA
Table[2*Sum[Floor[Sqrt[(n/2)^2 -k^2]], {k, Floor[n/2]}], {n, 100}]
PROG
(Magma)
A136513:= func< n | n eq 1 select 0 else 2*(&+[Floor(Sqrt((n/2)^2-j^2)): j in [1..Floor(n/2)]]) >;
[A136513(n): n in [1..100]]; // G. C. Greubel, Jul 27 2023
(SageMath)
def A136513(n): return 2*sum(isqrt((n/2)^2-k^2) for k in range(1, (n//2)+1))
[A136513(n) for n in range(1, 101)] # G. C. Greubel, Jul 27 2023
(PARI) a(n) = 2*sum(k=1, n\2, sqrtint((n/2)^2-k^2)); \\ Michel Marcus, Jul 27 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008
STATUS
approved