|
Search: id:A136485
|
|
|
| A136485 |
|
Number of unit square lattice cells enclosed by origin centered circle of diameter n. |
|
+0
4
|
|
| 0, 0, 4, 4, 12, 16, 24, 32, 52, 60, 76, 88, 112, 120, 148, 164, 192, 216, 256, 276, 308, 332, 376, 392, 440, 476, 524, 556, 608, 648, 688, 732, 796, 832, 904, 936, 1012, 1052, 1124, 1176, 1232, 1288, 1372, 1428, 1508, 1560, 1648, 1696, 1788, 1860, 1952, 2016
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
a(n) is the number of complete squares that fit inside the circle with diameter n, drawn on squared paper As n -> infinity, lim a(n)/(n^2) -> pi/4
|
|
FORMULA
|
a(n) = 4 * Sum floor(sqrt((n/2)^2 - k^2)), k = 1 .... floor(n/2)
|
|
EXAMPLE
|
a(3) = 4 because a circle centered at the origin and of radius 3/2 encloses (-1,-1),(-1,1),(1,-1),(1,1)
|
|
MATHEMATICA
|
Table[4*Sum[Floor[Sqrt[(n/2)^2 - k^2]], {k, 1, Floor[n/2]}], {n, 1, 100}]
|
|
CROSSREFS
|
Cf. a(n) = 4 * A136483 = 2 * A136513 alternating merge of A136485 and A119677.
Adjacent sequences: A136482 A136483 A136484 this_sequence A136486 A136487 A136488
Sequence in context: A109045 A079315 A121189 this_sequence A053415 A079902 A120033
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008
|
|
|
Search completed in 0.002 seconds
|
