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 A242118 Number of unit squares that intersect the circumference of a circle of radius n centered at (0,0). 9
 0, 4, 12, 20, 28, 28, 44, 52, 60, 68, 68, 84, 92, 92, 108, 108, 124, 124, 140, 148, 148, 164, 172, 180, 188, 180, 196, 212, 220, 220, 228, 244, 252, 260, 260, 268, 284, 284, 300, 300, 308, 316, 332, 340, 348, 348, 364, 372, 380, 388, 380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For the points that form the Pythagorean triple (for example see illustration n = 5, on the first quadrant at coordinate (4,3) and (3,4)), the transit of circumference occurs exactly at the corners, therefore there are no additional intersecting squares on the upper or lower rows (diagonally NE & SW directions) of such points. When the center of the circle is chosen at the middle of a square grid centered at (1/2,0), the sequence will be 2*A004767(n-1). LINKS Kival Ngaokrajang, Illustration of initial terms FORMULA a(n) = 4*Sum{k=1..n} ceiling(sqrt(n^2 - (k-1)^2)) - floor(sqrt(n^2 - k^2)). - Orson R. L. Peters, Jan 30 2017 a(n) = 8*n - A046109(n) for n > 0. - conjectured by Orson R. L. Peters, Jan 30 2017, proved by Andrey Zabolotskiy, Jan 31 2017 PROG (Python) a = lambda n: sum(4 for x in range(n) for y in range(n)                     if x**2 + y**2 < n**2 and (x+1)**2 + (y+1)**2 > n**2) (Python) from sympy import factorint def a(n):     r = 1     for p, e in factorint(n).items():         if p%4 == 1: r *= 2*e + 1     return 8*n - 4*r if n > 0 else 0 CROSSREFS Cf. A009003, A004767. Sequence in context: A285526 A321466 A227226 * A030387 A269931 A043437 Adjacent sequences:  A242115 A242116 A242117 * A242119 A242120 A242121 KEYWORD nonn AUTHOR Kival Ngaokrajang, May 05 2014 EXTENSIONS Terms corrected by Orson R. L. Peters, Jan 30 2017 STATUS approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)