A025465 -id:A025465 - cp's OEIS frontend

A025469 Number of partitions of n into 3 distinct positive cubes.

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

Offset: 0

David W. Wilson

nonn

In other words, number of solutions to the equation n = x^3 + y^3 + z^3 with x > y > z > 0. - Antti Karttunen, Aug 29 2017

			From _Antti Karttunen_, Aug 29 2017: (Start)
For n = 36 there is one solution: 36 = 27 + 8 + 1, thus a(36) = 1.
For n = 1009 there are two solutions: 1009 = 10^3 + 2^3 + 1^3 = 9^3 + 6^3 + 4^3, thus a(1009) = 2. This is also the first point where sequence attains value greater than one.
(End)

Antti Karttunen, Table of n, a(n) for n = 0..17073
Index entries for sequences related to sums of cubes

Cf. A025465 (not necessarily distinct), A025468, A025419 (greedy inverse).

Cf. A024975 (positions of nonzero terms), A024974 (positions of terms > 1), A025399-A025402.

A025469 := 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+1 do
            if x^3+2*y^3 > n then
                break;
            end if;
            zcu := n-x^3-y^3 ;
            if zcu > y^3 and isA000578(zcu) then
                a := a+1 ;
            end if;
        end do:
    end do:
end proc:
seq(A025469(n),n=1..80) ; # R. J. Mathar, Jun 15 2018

Table[Count[IntegerPartitions[n, {3}], ?(And[UnsameQ @@ #, AllTrue[#, IntegerQ[#^(1/3)] &]] &)], {n, 105}] (* _Michael De Vlieger, Aug 29 2017 *)

A025469(n) = { my(s=0); for(x=1,n,if(ispower(x,3),for(y=x+1,n-x,if(ispower(y,3),for(z=y+1,n-(x+y),if((ispower(z,3)&&(x+y+z)==n),s++)))))); (s); }; \\ Antti Karttunen, Aug 29 2017

a(n) = A025465(n) - A025468(n). - Antti Karttunen, Aug 29 2017

A025468 a(n) is the number of partitions of n into 2 distinct positive cubes.

Original entry on oeis.org

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

Offset: 0

David W. Wilson

nonn

In other words, number of solutions to the equation n = x^3 + y^3 with x > y > 0. The first value > 1 is a(1729) = 2. - Antti Karttunen, Aug 29 2017

Antti Karttunen, Table of n, a(n) for n = 0..100000
Index entries for sequences related to sums of cubes

Cf. A000578, A048766, A025455, A025465, A025469.

(define (A025468 n) (let loop ((x (A048766 n)) (s 0)) (let* ((x3 (A000578 x)) (y3 (- n x3))) (if (<= x3 y3) s (loop (- x 1) (+ s (if (and (> y3 0) (= (A000578 (A048766 y3)) y3)) 1 0))))))) ;; Antti Karttunen, Aug 28 2017

From Antti Karttunen, Aug 28-29 2017: (Start)
a(n) = A025465(n) - A025469(n).
a(n) <= A025455(n).
(End)

A025466 Number of partitions of n into 4 distinct nonnegative cubes.

Original entry on oeis.org

Offset: 0

David W. Wilson

nonn

In other words, number of solutions to the equation n = w^3 + x^3 + y^3 + z^3 with w > x > y > z >= 0. - Antti Karttunen, Sep 21 2018

			For n=540 we have two solutions: 540 = (0^3 + 1^3 + 3^3 + 8^3) = (2^3 + 4^3 + 5^3 + 7^3), thus a(540) = 2. This is the first point where a(n) > 1. - _Antti Karttunen_, Sep 21 2018

Antti Karttunen, Table of n, a(n) for n = 0..12121

Cf. A000578, A025465.

A025466(n) = { my(s=0); for(w=0,n,if(ispower(w,3),for(x=w+1,n-w,if(ispower(x,3),for(y=x+1,n-(w+x),if(ispower(y,3),for(z=y+1,n-(w+x+y),if((ispower(z,3)&&(w+x+y+z)==n),s++)))))))); (s); }; \\ Antti Karttunen, Sep 21 2018

Secondary offset added by Antti Karttunen, Sep 21 2018

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A025469 Number of partitions of n into 3 distinct positive cubes.

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A025468 a(n) is the number of partitions of n into 2 distinct positive cubes.

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A025466 Number of partitions of n into 4 distinct nonnegative cubes.

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