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

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

Author

David W. Wilson

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Programs

Scheme

(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

Formula

From Antti Karttunen, Aug 28-29 2017: (Start)

a(n) = A025465(n) - A025469(n).

a(n) <= A025455(n).

(End)