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A124623 Number of unit squares having center within inscribed circle of an n X n integer square. 1
1, 4, 9, 12, 21, 32, 37, 52, 69, 80, 97, 112, 137, 156, 177, 208, 225, 256, 293, 316, 349, 384, 421, 448, 489, 540, 577, 616, 665, 716, 749, 812, 861, 912, 973, 1020, 1085, 1124, 1201, 1264, 1313, 1396, 1457, 1528, 1597, 1664, 1741, 1804, 1885, 1976, 2053, 2128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Robert G. Wilson v, Mar 22 2017: (Start)

For n odd, the center of the circle is in the middle of the center square and thus a(2n-1) == 1 (mod 4).

For n even, the center of the circle is at the four corners of the center 4 squares and thus a(2n) == 0 (mod 4).

a(n) ~ n*Pi/4. (End)

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n^2 - 4*k(n); k(n) = number of exterior centers per quadrant.

a(2n-1) = A036704(n-1). - Robert G. Wilson v, Mar 28 2017

a(2n) = 4*A120883(n-1). - Robert G. Wilson v, Mar 28 2017

MATHEMATICA

f[n_] := 4*Length[ Select[ Flatten[ Table[ If[ OddQ@ n, x^2 + y^2, x(x -1) + y(y -1) + 1/2], {x, n/2}, {y, n/2}]], 4# < n^2 &]] + If[ OddQ@ n, 2(n -1) + 1, 0]; Array[f, 52] (* Robert G. Wilson v, Mar 22 2017 *)

CROSSREFS

Cf. A051233.

Sequence in context: A119640 A186130 A051233 * A220195 A221355 A197681

Adjacent sequences:  A124620 A124621 A124622 * A124624 A124625 A124626

KEYWORD

easy,nonn

AUTHOR

William A. Berry (waberr2(AT)uky.edu), Dec 21 2006

STATUS

approved

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Last modified May 19 14:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)