A025457 Number of partitions of n into 4 positive cubes.

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, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1

Offset

0,220

Comments

The first term > 1 is a(219) = 2. - Michel Marcus, Apr 23 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^4] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019

Maple

N:= 100;
A:= Array(0..N);
for a from 1 to floor(N^(1/3)) do
  for b from a to floor((N-a^3)^(1/3)) do
     for c from b to floor((N-a^3-b^3)^(1/3)) do
        for d from c to floor((N-a^3-b^3-c^3)^(1/3)) do
          n:= a^3 + b^3 + c^3 + d^3;
          A[n]:= A[n]+1;
od od od od:
seq(A[n], n=0..N); # Robert Israel, Aug 18 2014
A025457 := proc(n)
    local a, x, y, z, ucu ;
    a := 0 ;
    for x from 1 do
        if 4*x^3 > n then
            return a;
        end if;
        for y from x do
            if x^3+3*y^3 > n then
                break;
            end if;
            for z from y do
                if x^3+y^3+2*z^3 > n then
                    break;
                end if;
                ucu := n-x^3-y^3-z^3 ;
                if isA000578(ucu) then
                    a := a+1 ;
                end if;
            end do:
        end do:
    end do:
end proc: # R. J. Mathar, Sep 15 2015

Mathematica

r[n_] := Reduce[0 < a <= b <= c <= d && n == a^3+b^3+c^3+d^3, {a, b, c, d}, Integers];
a[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
Table[a[n], {n, 0, 107}] (* Jean-François Alcover, Feb 26 2019 *)

Crossrefs

Cf. A003108, A025455, A025456, A025403-A025407, A003327, A025420 (greedy inverse).

Sequence in context: A359150 A354031 A354035 * A350289 A219463 A286688

Adjacent sequences: A025454 A025455 A025456 * A025458 A025459 A025460

Keyword

nonn

Author

David W. Wilson

Extensions

Second offset from Michel Marcus, Apr 23 2019

Status

approved