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A025455
a(n) is the number of partitions of n into 2 positive cubes.
9
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, 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, 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
0,1730
COMMENTS
In other words, number of solutions to the equation x^3 + y^3 = n with x >= y > 0. - Antti Karttunen, Aug 28 2017
The first term > 1 is a(1729) = 2. - Michel Marcus, Apr 23 2019
FORMULA
If a(n) > 0 then A025456(n + k^3) > 0 for k>0; a(A113958(n)) > 0; a(A003325(n)) > 0. - Reinhard Zumkeller, Jun 03 2006
a(n) >= A025468(n). - Antti Karttunen, Aug 28 2017
a(n) = [x^n y^2] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
MATHEMATICA
Table[Count[IntegerPartitions[n, {2}], _?(AllTrue[Surd[#, 3], IntegerQ]&)], {n, 0, 110}] (* Harvey P. Dale, Nov 23 2022 *)
PROG
(Scheme) (define (A025455 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
CROSSREFS
Cf. A025456, A025468, A003108, A003325, A000578, A048766, A001235 (two or more ways, positions where a(n) > 1).
Cf. also A025426, A216284.
Sequence in context: A328794 A185706 A358759 * A288167 A288991 A289016
KEYWORD
nonn
EXTENSIONS
Secondary offset added by Antti Karttunen, Aug 28 2017
Secondary offset corrected by Michel Marcus, Apr 23 2019
STATUS
approved