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A025456 Number of partitions of n into 3 positive cubes. 16
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, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,252

COMMENTS

If A025455(n) > 0 then a(n + k^3) > 0 for k>0; a(A119977(n))>0; a(A003072(n))>0. - Reinhard Zumkeller, Jun 03 2006

a(A057904(n))=0; a(A003072(n))>0; a(A025395(n))=1; a(A008917(n))>1; a(A025396(n))=2. - Reinhard Zumkeller, Apr 23 2009

The first term > 1 is a(251) = 2. - Michel Marcus, Apr 23 2019

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of cubes

FORMULA

a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019

MAPLE

A025456 := proc(n)

    local a, x, y, zcu ;

    a := 0 ;

    for x from 1 do

        if 3*x^3 > n then

            return a;

        end if;

        for y from x do

            if x^3+2*y^3 > n then

                break;

            end if;

            zcu := n-x^3-y^3 ;

            if isA000578(zcu) then

                a := a+1 ;

            end if;

        end do:

    end do:

end proc: # R. J. Mathar, Sep 15 2015

MATHEMATICA

a[n_] := Count[ PowersRepresentations[n, 3, 3], pr_List /; FreeQ[pr, 0]]; Table[a[n], {n, 0, 107}] (* Jean-Fran├žois Alcover, Oct 31 2012 *)

PROG

(PARI) a(n)=sum(a=sqrtnint(n\3, 3), sqrtnint(n, 3), sum(b=1, a, my(C=n-a^3-b^3, c); ispower(C, 3, &c)&&0<c&&c<=b)) \\ Charles R Greathouse IV, Jun 26 2013

CROSSREFS

Least inverses are A025418.

Cf. A025455, A003108, A003072 (1 or more ways), A008917 (two or more ways), A025395-A025398.

Sequence in context: A160753 A328981 A024360 * A288314 A285963 A024889

Adjacent sequences:  A025453 A025454 A025455 * A025457 A025458 A025459

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Second offset from Michel Marcus, Apr 23 2019

STATUS

approved

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Last modified November 14 10:04 EST 2019. Contains 329111 sequences. (Running on oeis4.)