This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A025446 #27 Jun 24 2024 23:28:53 %S A025446 1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0, %T A025446 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0, %U A025446 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1 %N A025446 Number of partitions of n into 2 nonnegative cubes. %C A025446 a(1729) = 2, the first point where a value larger than 1 appears, and where this sequence differs from A373972. - _Antti Karttunen_, Jun 24 2024 %H A025446 Antti Karttunen, <a href="/A025446/b025446.txt">Table of n, a(n) for n = 0..100080</a> %H A025446 Wikipedia, <a href="https://en.wikipedia.org/wiki/1729_(number)">1729 (number)</a> %F A025446 a(n) = A010057(n) + A025455(n) = A010057(n) XOR A025455(n). [The latter by Fermat's Last Theorem] - _Antti Karttunen_, Jun 24 2024 %e A025446 From _Antti Karttunen_, Jun 24 2024: (Start) %e A025446 8 = 0^3 + 2^3, and as there are no other partitions of 8 into 2 nonnegative cubes, a(8) = 1. %e A025446 16 = 2^3 + 2^3, and as there are no other partitions of 16 into 2 nonnegative cubes, a(16) = 1. %e A025446 1729 = 1^3 + 12^3 = 9^3 + 10^3, and as there are no other partitions of 1729 into 2 nonnegative cubes, a(1729) = 2. %e A025446 (End) %o A025446 (PARI) A025446(n) = if(n<=2, 1, my(s=0, x=sqrtnint(n,3)); forstep(i=x, 0, -1, my(x3=i^3, y3=n-x3); if(y3>x3, return(s), s += ispower(y3, 3)))); \\ _Antti Karttunen_, Jun 24 2024 %Y A025446 Cf. A010057, A025455, A004999 (indices of nonzero terms), A373972 (their characteristic function). %K A025446 nonn %O A025446 0,1730 %A A025446 _David W. Wilson_ %E A025446 Data section extended up to a(126) and the secondary offset added by _Antti Karttunen_, Jun 24 2024