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 A136485 Number of unit square lattice cells enclosed by origin centered circle of diameter n. 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; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS FORMULA a(n) = 4 * Sum_{k=1..floor(n/2)} floor(sqrt((n/2)^2 - k^2)). a(n) = [x^(n^2)] (theta_3(x^4) - 1)^2 / (1 - x). - Ilya Gutkovskiy, Nov 24 2021 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 Equals 4 * A136483 = 2 * A136513. Alternating merge of A136485 and A119677. Sequence in context: A282503 A323189 A121189 * A157617 A053415 A303315 Adjacent sequences:  A136482 A136483 A136484 * A136486 A136487 A136488 KEYWORD easy,nonn AUTHOR Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008 STATUS approved

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Last modified June 26 18:18 EDT 2022. Contains 354885 sequences. (Running on oeis4.)