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 A303644 a(n) is the number of lattice points in a Cartesian grid between a square of side length 2*n, centered at the origin, and its inscribed circle. The sides of the square are parallel to the coordinate axes. 4
 0, 0, 0, 4, 4, 12, 24, 32, 40, 48, 68, 92, 100, 120, 136, 168, 192, 220, 244, 268, 312, 336, 376, 420, 444, 484, 524, 576, 624, 664, 724, 764, 820, 868, 912, 992, 1040, 1116, 1156, 1220, 1304, 1368, 1440, 1496, 1564, 1660, 1732, 1816, 1888, 1960, 2032, 2116, 2220, 2308 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The borders of the square and the circle are not included. Rotating the square by 45 degrees (so that its vertices lie on the coordinate axes) results in sequence A303646 instead. LINKS Table of n, a(n) for n=1..54. Kirill Ustyantsev, illustrated example FORMULA a(n) = A016754(n-1) - A000328(n) - 4. EXAMPLE For n = 4, we have 4 points with integer coordinates; the point in the first quadrant is at (3,3): . o . . + . . o . . . + . . . . . . + . . . -+-+-+-+-+-+-+- . . . + . . . . . . + . . . o . . + . . o . Similarly, for n = 5, we have 4 points with integer coordinates; the point in the first quadrant is at (4,4): . o . . . + . . . o . . . . + . . . . . . . . + . . . . . . . . + . . . . -+-+-+-+-+-+-+-+-+- . . . . + . . . . . . . . + . . . . . . . . + . . . . o . . . + . . . o . For n = 6, we have 12 points, of which the 3 points in the first quadrant are at (4,5), (5,4), and (5,5): . o o . . . + . . . o o o . . . . + . . . . o . . . . . + . . . . . . . . . . + . . . . . . . . . . + . . . . . -+-+-+-+-+-+-+-+-+-+-+- . . . . . + . . . . . . . . . . + . . . . . . . . . . + . . . . . o . . . . + . . . . o o o . . . + . . . o o PROG (Python) import math for n in range(1, 100): count = 0 for x in range(1, n): for y in range(1, n): if x * x + y * y > n * n and x < n and y < n: count = count + 1 print(4 * count, end=", ") (PARI) a(n) = sum(x=-n+1, n-1, sum(y=-n+1, n-1, (x^2+y^2) > n^2)); \\ Michel Marcus, May 22 2018 CROSSREFS Cf. A000328, A016754, A302829, A303642, A303646. Sequence in context: A120033 A097073 A019085 * A298796 A106232 A359709 Adjacent sequences: A303641 A303642 A303643 * A303645 A303646 A303647 KEYWORD nonn AUTHOR Kirill Ustyantsev, Apr 27 2018 STATUS approved

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Last modified September 8 21:25 EDT 2024. Contains 375759 sequences. (Running on oeis4.)