The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212098 Number of (w,x,y,z) with all terms in {1,...,n} and w^3<=x^3+y^3+z^3. 3
0, 1, 15, 72, 221, 536, 1104, 2034, 3451, 5514, 8380, 12246, 17322, 23812, 31981, 42107, 54457, 69350, 87100, 108049, 132591, 161085, 193966, 231592, 274511, 323077, 377830, 439314, 507948, 584401, 669124, 762764, 865882, 979130 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(n)+A212099(n)=n^4. For a guide to related sequences, see A211795.
LINKS
MAPLE
f:= proc(n) local x, y, z, r, t;
r:= 0:
for x from 1 to n do
for y from x to n do
for z from y to n do
t:= min(n, floor((x^3 + y^3 + z^3)^(1/3)));
if x = z then r:= r+t
elif x=y or y=z then r:= r+3*t
else r:= r+6*t
fi
od od od;
r
end proc:
map(f, [$0..40]); # Robert Israel, May 08 2017
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^3 <= x^3 + y^3 + z^3, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212098 *)
(* Peter J. C. Moses, Apr 13 2012 *)
PROG
(PARI) A212098(n)={my(s=0, c=[6, 3, 1]); forvec(v=vector(4, i, if(i>1, [1, n], [-n, -1])), sum(i=1, 4, v[i]^3)>=0&s+=c[1+(v[2]==v[3])+(v[3]==v[4])], 1); s} /* not very efficient */ M. F. Hasler, May 20 2012
CROSSREFS
Sequence in context: A126274 A241234 A212097 * A053531 A000476 A002603
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 03 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 04:20 EDT 2024. Contains 372782 sequences. (Running on oeis4.)