A333573 -id:A333573 - 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

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.

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