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A303646
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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.
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4
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0, 0, 12, 12, 32, 32, 32, 68, 60, 104, 104, 104, 156, 148, 216, 216, 300, 292, 276, 368, 368, 468, 460, 452, 560, 544, 676, 668, 816, 792, 784, 932, 916, 1080, 1048, 1048, 1220, 1212, 1384, 1360, 1352, 1556, 1532, 1736, 1704, 1956, 1924, 1900, 2136, 2096, 2340, 2308
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OFFSET
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1,3
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COMMENTS
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Rotating the square by 45 degrees (so that its vertices lie on the coordinate axes) results in sequence A303644 instead.
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LINKS
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PROG
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(Python)
import math
for n in range (1, 100):
sqn = math.ceil(math.sqrt(2)*n)
count = 0
for x in range(-sqn, sqn):
for y in range(-sqn, sqn):
if (x*x+y*y>n*n and abs(x)+abs(y)<n*math.sqrt(2)):
count += 1
print(count)
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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