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A136484 Number of unit square lattice cells inside quadrant of origin centered circle of diameter 2n+1. 3
0, 1, 3, 6, 13, 19, 28, 37, 48, 64, 77, 94, 110, 131, 152, 172, 199, 226, 253, 281, 308, 343, 377, 412, 447, 488, 528, 567, 612, 654, 703, 750, 796, 847, 902, 957, 1013, 1068, 1129, 1187, 1252, 1313, 1378, 1446, 1511, 1582, 1650, 1725, 1800, 1877, 1955, 2034 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of unit square lattice cells inside quadrant of origin centered circle of radius n+1/2 As n -> infinity, lim a(n)/(n^2) -> pi/16

LINKS

Table of n, a(n) for n=0..51.

FORMULA

a(n) = Sum(floor(sqrt((n+1/2)^2 - k^2))), k = 1 ... n

EXAMPLE

a(2) = 3 because a circle of radius 2+1/2 in the first quadrant encloses (2,1),(1,1),(1,2)

MATHEMATICA

Table[Sum[Floor[Sqrt[(n + 1/2)^2 - k^2]], {k, 1, n}], {n, 0, 100}]

CROSSREFS

Cf. a(n) = 1/2 * A136515 = 1/4 * A136486 odd terms of A136483.

Sequence in context: A078382 A075651 A091277 * A263621 A137039 A137035

Adjacent sequences:  A136481 A136482 A136483 * A136485 A136486 A136487

KEYWORD

easy,nonn

AUTHOR

Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008

STATUS

approved

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Last modified September 26 05:46 EDT 2022. Contains 356986 sequences. (Running on oeis4.)