OFFSET
1,5
LINKS
Ivan Panchenko, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = Sum_{k=1..floor(n/2)} floor(sqrt((n/2)^2 - k^2)).
Lim_{n -> oo} a(n)/(n^2) -> Pi/16 (A019683).
a(n) = [x^(n^2)] (theta_3(x^4) - 1)^2 / (4 * (1 - x)). - Ilya Gutkovskiy, Nov 23 2021
EXAMPLE
a(5) = 3 because a circle of radius 5/2 in the first quadrant encloses (2,1), (1,1), (1,2).
MATHEMATICA
Table[Sum[Floor[Sqrt[(n/2)^2 -k^2]], {k, Floor[n/2]}], {n, 100}]
PROG
(Magma)
A136483:= func< n | n eq 1 select 0 else (&+[Floor(Sqrt((n/2)^2-j^2)): j in [1..Floor(n/2)]]) >;
[A136483(n): n in [1..100]]; // G. C. Greubel, Jul 28 2023
(SageMath)
def A136483(n): return sum(isqrt((n/2)^2-j^2) for j in range(1, (n//2)+1))
[A136483(n) for n in range(1, 101)] # G. C. Greubel, Jul 28 2023
(PARI) a(n) = sum(k=1, n\2, sqrtint((n/2)^2 - k^2)); \\ Michel Marcus, Jul 28 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008
STATUS
approved