A232705 -id:A232705 - cp's OEIS frontend

A333462 a(n) is the number of Gaussian integers z such that (n-1)/2 < |z| <= n/2, divided by 4.

0, 1, 1, 1, 2, 2, 2, 3, 5, 3, 4, 4, 6, 3, 7, 5, 7, 7, 10, 6, 8, 7, 11, 5, 12, 10, 12, 9, 13, 11, 10, 12, 16, 10, 18, 9, 19, 11, 18, 14, 14, 15, 21, 15, 20, 14, 22, 13, 23, 19, 23, 17, 24, 18, 22, 19, 27, 17, 26, 22, 28, 17, 31, 21, 26, 24, 28, 26, 30, 27, 29, 21

Offset: 1

Hugo Pfoertner, Mar 26 2020

nonn

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Cf. A004018, A232705, A333572, A333573.

c=vectorsmall(2000000);for(x=1,1000,my(x2=x*x);c[x2]++;c[x2+x2]++;for(y=1,x-1,my(y2=y*y);c[x2+y2]+=2));
a(n)=sum(k=ceil((1+(n-1)^2)/4),floor(n^2/4),c[k]);
for(k=1,72,print1(a(k),", "))

A333572 a(n) is the number of Gaussian integers z with 0 < |z| <= n/2.

Original entry on oeis.org

0, 4, 8, 12, 20, 28, 36, 48, 68, 80, 96, 112, 136, 148, 176, 196, 224, 252, 292, 316, 348, 376, 420, 440, 488, 528, 576, 612, 664, 708, 748, 796, 860, 900, 972, 1008, 1084, 1128, 1200, 1256, 1312, 1372, 1456, 1516, 1596, 1652, 1740, 1792, 1884, 1960, 2052, 2120

Offset: 1

Hugo Pfoertner, Mar 27 2020

nonn

Robert Israel, Table of n, a(n) for n = 1..2000

Cf. A004018, A232705, A333462, A333573.

N:= 100: # for a(1)..a(N)
V:= Vector(N):
for x from 1 to N/2 do
  for y from 0 to x do
    v:= ceil(2*sqrt(x^2+y^2));
    if v > N then break fi;
    if y=x or y=0 then V[v]:= V[v]+4 else V[v]:= V[v]+8 fi
od od:
ListTools:-PartialSums(convert(V,list)); # Robert Israel, Mar 29 2020

A333573 a(n) = A333572(n)/4.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 12, 17, 20, 24, 28, 34, 37, 44, 49, 56, 63, 73, 79, 87, 94, 105, 110, 122, 132, 144, 153, 166, 177, 187, 199, 215, 225, 243, 252, 271, 282, 300, 314, 328, 343, 364, 379, 399, 413, 435, 448, 471, 490, 513, 530, 554, 572, 594, 613, 640, 657

Offset: 1

Hugo Pfoertner, Mar 27 2020

nonn

Robert Israel, Table of n, a(n) for n = 1..2000

Cf. A004018, A232705, A333462, A333572.

A036705 Number of Gaussian integers z=a+bi satisfying n - 1/2 < |z| <= n + 1/2.

Original entry on oeis.org

1, 8, 12, 16, 32, 28, 40, 40, 48, 68, 56, 72, 68, 88, 88, 84, 112, 112, 112, 116, 112, 144, 140, 144, 144, 168, 164, 160, 184, 172, 200, 192, 188, 208, 224, 224, 228, 224, 248, 236, 264, 248, 264, 276, 264, 288, 276, 304, 304, 312

Offset: 0

Clark Kimberling

nonn

Number of integer Cartesian grid points covered by a ring around the origin with width 1 and outer radius n + 1/2. - Ralf Stephan, Nov 28 2013

Index entries for Gaussian integers and primes

Cf. A047077, A232705.

a[n_] := If[n==0, 1, inf = (n-1/2)^2; sup = (n+1/2)^2; 4 Sum[Boole[inf < x^2 + y^2 < sup], {x, 0, n}, {y, 1, n}]];
a /@ Range[0, 49] (* Jean-François Alcover, Nov 14 2019 *)

a(n)=sum(i=-n, n, sum(j=-n, n, d=sqrt(i*i+j*j); if(d>=n-1/2&&d<=n+1/2, 1))) \\ Ralf Stephan, Nov 28 2013

Edited by Ralf Stephan, Nov 28 2013

cp's OEIS Frontend

A333462 a(n) is the number of Gaussian integers z such that (n-1)/2 < |z| <= n/2, divided by 4.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A333572 a(n) is the number of Gaussian integers z with 0 < |z| <= n/2.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

A333573 a(n) = A333572(n)/4.

Views

Author

Keywords

Links

Crossrefs

A036705 Number of Gaussian integers z=a+bi satisfying n - 1/2 < |z| <= n + 1/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions