login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A025457 Number of partitions of n into 4 positive cubes. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 26 2019 *)

CROSSREFS

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

Sequence in context: A023971 A330551 A079260 * A219463 A286688 A285125

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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:10 EDT 2020. Contains 333089 sequences. (Running on oeis4.)