login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A303646 a(n) is the number of lattice points in a Cartesian grid between a square with integer sides 2*n and its inscribed circle. The sides of the square are parallel to the bisector of coordinate axes. 4

%I #23 Jun 09 2020 09:28:44

%S 0,0,12,12,32,32,32,68,60,104,104,104,156,148,216,216,300,292,276,368,

%T 368,468,460,452,560,544,676,668,816,792,784,932,916,1080,1048,1048,

%U 1220,1212,1384,1360,1352,1556,1532,1736,1704,1956,1924,1900,2136,2096,2340,2308

%N a(n) is the number of lattice points in a Cartesian grid between a square with integer sides 2*n and its inscribed circle. The sides of the square are parallel to the bisector of coordinate axes.

%C Rotating the square by 45 degrees (so that its vertices lie on the coordinate axes) results in sequence A303644 instead.

%H Kirill Ustyantsev, <a href="https://www.desmos.com/calculator/esxgfyvpj3">Graphic illustration</a>

%o (Python)

%o import math

%o for n in range (1, 100):

%o sqn = math.ceil(math.sqrt(2)*n)

%o count = 0

%o for x in range(-sqn, sqn):

%o for y in range(-sqn, sqn):

%o if (x*x+y*y>n*n and abs(x)+abs(y)<n*math.sqrt(2)):

%o count += 1

%o print(count)

%o (PARI) a(n) = sum(x=-2*n, 2*n, sum(y=-2*n, 2*n, ((x^2+y^2) > n^2) && ((abs(x)+abs(y))^2 < 2*n^2))); \\ _Michel Marcus_, May 22 2018

%Y Cf. A302829, A303642, A303644.

%K nonn

%O 1,3

%A _Kirill Ustyantsev_, Apr 27 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)