A053593 Closed 3-dimensional ball numbers (version 2): a(n)= number of integer points (i,j,k) contained in a closed ball of diameter n, centered at (1/2,0,0).

0, 2, 2, 20, 28, 70, 110, 192, 256, 402, 498, 708, 884, 1166, 1422, 1800, 2104, 2594, 3026, 3588, 4140, 4918, 5542, 6432, 7224, 8186, 9122, 10380, 11460, 12790, 14094, 15624, 17080, 18882, 20458, 22500, 24364, 26590, 28678, 31136, 33400

Offset

0,2

Comments

a(n)/(n/2)^3->4/3*Pi

Links

Robert Israel, Table of n, a(n) for n = 0..2000

Maple

N:= 100: # to get a(0)..a(N)
B:= Array(0..N^2):
B[0]:= 1:
for x from 1 to N do
  for y from 0 to x do
    r:= x^2 + y^2;
    if r > N^2 then break fi;
    if y=0 or y=x then B[r]:= B[r]+4 else B[r]:= B[r]+8 fi
od od:
BL:= convert(B, list):
SL:= ListTools:-PartialSums(BL):
f:= n ->   add(SL[floor((n^2+3)/4-x^2+x)], x=ceil(1/2-n/2)..n/2+1/2):
seq(f(n), n=0..N); # Robert Israel, Apr 09 2018

Crossrefs

Sequence in context: A103129 A322898 A009340 * A002907 A350466 A184717

Adjacent sequences: A053590 A053591 A053592 * A053594 A053595 A053596

Keyword

easy,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 19 2000

Status

approved