A025458 Number of partitions of n into 5 positive cubes.

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

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of cubes

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

Adjacent sequences: A025455 A025456 A025457 * A025459 A025460 A025461

Keyword

nonn

Author

David W. Wilson

Extensions

Second offset from Michel Marcus, Apr 25 2019

Status

approved