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%I #35 Nov 23 2022 19:39:13
%S 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,
%T 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,
%U 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
%N a(n) is the number of partitions of n into 2 positive cubes.
%C In other words, number of solutions to the equation x^3 + y^3 = n with x >= y > 0. - _Antti Karttunen_, Aug 28 2017
%C The first term > 1 is a(1729) = 2. - _Michel Marcus_, Apr 23 2019
%H Antti Karttunen, <a href="/A025455/b025455.txt">Table of n, a(n) for n = 0..100000</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F 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
%F a(n) >= A025468(n). - _Antti Karttunen_, Aug 28 2017
%F a(n) = [x^n y^2] Product_{k>=1} 1/(1 - y*x^(k^3)). - _Ilya Gutkovskiy_, Apr 23 2019
%t Table[Count[IntegerPartitions[n,{2}],_?(AllTrue[Surd[#,3],IntegerQ]&)],{n,0,110}] (* _Harvey P. Dale_, Nov 23 2022 *)
%o (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
%Y Cf. A025456, A025468, A003108, A003325, A000578, A048766, A001235 (two or more ways, positions where a(n) > 1).
%Y Cf. also A025426, A216284.
%K nonn
%O 0,1730
%A _David W. Wilson_
%E Secondary offset added by _Antti Karttunen_, Aug 28 2017
%E Secondary offset corrected by _Michel Marcus_, Apr 23 2019
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