A001182 Number of cells of square lattice of edge 1/n inside quadrant of unit circle centered at 0.

0, 1, 4, 8, 15, 22, 30, 41, 54, 69, 83, 98, 119, 139, 162, 183, 208, 234, 263, 294, 322, 357, 390, 424, 465, 504, 545, 585, 628, 675, 719, 770, 819, 872, 928, 977, 1036, 1090, 1155, 1216, 1274, 1339, 1404, 1475, 1545, 1610, 1683, 1755, 1832, 1911, 1992, 2072

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n-1} floor(sqrt(n^2-k^2)). - Horst Kraemer (horst.kraemer(AT)epost.de) Apr 07 2004

a(n) = A261849(2*n)/4 = (A281795(n)-A242118(n))/4. - Andrey Zabolotskiy, Jan 30 2017

a(n) = [x^(n^2)] (theta_3(x) - 1)^2/(4*(1 - x)), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 17 2018

Mathematica

Table[Sum[Floor@ Sqrt[n^2 - k^2], {k, n - 1}], {n, 52}] (* Michael De Vlieger, Jan 30 2017 *)

Prog

(Python)
from math import isqrt
def A001182(n): return sum(isqrt(k*((n<<1)-k)) for k in range(1, n)) # Chai Wah Wu, Jul 18 2024

Crossrefs

Cf. A261849, A242118, A281795.

Sequence in context: A024916 A212539 A102216 * A264599 A375195 A122247

Adjacent sequences: A001179 A001180 A001181 * A001183 A001184 A001185

Keyword

nonn

Author

Tihamer von Ghyczy (ghyczy(AT)esinet.net)

Extensions

More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000

Status

approved