|
|
A136486
|
|
Number of unit square lattice cells enclosed by origin centered circle of diameter 2n+1.
|
|
3
|
|
|
0, 4, 12, 24, 52, 76, 112, 148, 192, 256, 308, 376, 440, 524, 608, 688, 796, 904, 1012, 1124, 1232, 1372, 1508, 1648, 1788, 1952, 2112, 2268, 2448, 2616, 2812, 3000, 3184, 3388, 3608, 3828, 4052, 4272, 4516, 4748, 5008, 5252, 5512, 5784, 6044, 6328, 6600
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(n) is the number of complete squares that fit inside the circle with radius n+1/2, drawn on squared paper.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*Sum_{k=1..n} floor(sqrt((n+1/2)^2 - k^2)).
Lim_{n -> oo} a(n)/(n^2) -> Pi/4 (A003881).
|
|
EXAMPLE
|
a(1) = 4 because a circle centered at the origin and of radius 1+1/2 encloses (-1,-1), (-1,1), (1,-1), (1,1).
|
|
MATHEMATICA
|
Table[4*Sum[Floor[Sqrt[(n + 1/2)^2 - k^2]], {k, n}], {n, 0, 100}]
|
|
PROG
|
(Magma)
A136486:= func< n | n eq 0 select 0 else 4*(&+[Floor(Sqrt((n+1/2)^2-j^2)): j in [1..n]]) >;
(SageMath)
def A136486(n): return 4*sum(floor(sqrt((n+1/2)^2-k^2)) for k in range(1, n+1))
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008
|
|
STATUS
|
approved
|
|
|
|