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 A025469 Number of partitions of n into 3 distinct positive cubes. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 LINKS Antti Karttunen, Table of n, a(n) for n = 0..17073 FORMULA a(n) = A025465(n) - A025468(n). - Antti Karttunen, Aug 29 2017 EXAMPLE 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) MAPLE 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 MATHEMATICA Table[Count[IntegerPartitions[n, {3}], _?(And[UnsameQ @@ #, AllTrue[#, IntegerQ[#^(1/3)] &]] &)], {n, 105}] (* Michael De Vlieger, Aug 29 2017 *) PROG (PARI) 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 CROSSREFS Cf. A025465 (not necessarily distinct), A025468, A025419 (greedy inverse). Cf. A024975 (positions of nonzero terms), A024974 (positions of terms > 1), A025399-A025402. Sequence in context: A248805 A307721 A023976 * A025466 A072769 A322437 Adjacent sequences:  A025466 A025467 A025468 * A025470 A025471 A025472 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)