login
A025458
Number of partitions of n into 5 positive cubes.
3
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
OFFSET
0,158
COMMENTS
a(n) > 2 at n= 766, 810, 827, 829, 865, 883, 981, 1018, 1025, 1044,... - R. J. Mathar, Sep 15 2015
The first term > 1 is a(157) = 2. - Michel Marcus, Apr 25 2019
FORMULA
a(n) = [x^n y^5] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
MAPLE
A025458 := proc(n)
local a, x, y, z, u, vcu ;
a := 0 ;
for x from 1 do
if 5*x^3 > n then
return a;
end if;
for y from x do
if x^3+4*y^3 > n then
break;
end if;
for z from y do
if x^3+y^3+3*z^3 > n then
break;
end if;
for u from z do
if x^3+y^3+z^3+2*u^3 > n then
break;
end if;
vcu := n-x^3-y^3-z^3-u^3 ;
if isA000578(vcu) then
a := a+1 ;
end if;
end do:
end do:
end do:
end do:
end proc: # R. J. Mathar, Sep 15 2015
MATHEMATICA
a[n_] := IntegerPartitions[n, {5}, Range[n^(1/3) // Ceiling]^3] // Length;
a /@ Range[0, 157] (* Jean-François Alcover, Jun 20 2020 *)
CROSSREFS
Column 5 of A320841, which cross-references the equivalent sequences for other numbers of positive cubes.
Positions of values: A057906 (0), A003328 (nonzero), A048926 (1), A048927 (2), A343705 (3), A344035 (4).
Sequence in context: A373383 A078926 A324824 * A378449 A286925 A378598
KEYWORD
nonn
EXTENSIONS
Second offset from Michel Marcus, Apr 25 2019
STATUS
approved