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A036693 Number of Gaussian integers z = a + bi satisfying n-1 < |z| <= n. 2
1, 4, 8, 16, 20, 32, 32, 36, 48, 56, 64, 60, 64, 88, 84, 96, 88, 104, 108, 120, 128, 116, 144, 136, 140, 168, 160, 168, 164, 176, 192, 180, 208, 200, 216, 228, 200, 240, 220, 264, 248, 236, 264, 264, 288, 284, 264, 296, 292, 312 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for Gaussian integers and primes

FORMULA

From Reinhard Zumkeller, Jan 13 2002: (Start)

a(n)/n ~ 2*Pi.

a(n) = A000328(n)-A000328(n-1). (End)

EXAMPLE

a(10^2) = 660, a(10^3) = 6392, a(10^4) = 62952, a(10^5) = 628520, a(10^6) = 6281404. - Reinhard Zumkeller, Jan 13 2002

PROG

(MAGMA)

[#[<x, y>: x in [-n..n], y in [-n..n]| n-1 lt r and r  le n where r is Sqrt(x^2+ y^2)]: n in [0..50]]; // Marius A. Burtea, Feb 18 2020

(Sage)

def A036693(n):

    if n == 0: return 1

    Range = lambda n: ((i, j) for i in (-n..n) for j in (-n..n))

    return sum(1 for (j, k) in Range(n) if (n-1)^2 < j^2 + k^2 <= n^2)

print([A036693(n) for n in range(20)]) # Peter Luschny, Mar 27 2020

CROSSREFS

Cf. A000328.

Sequence in context: A092259 A312805 A312806 * A181471 A272753 A272804

Adjacent sequences:  A036690 A036691 A036692 * A036694 A036695 A036696

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified April 13 17:30 EDT 2021. Contains 342936 sequences. (Running on oeis4.)