A286351 - OEIS

%I #14 May 09 2017 10:54:34

%S 0,0,1,0,1,0,1,0,1,0,2,0,1,0,2,0,1,6,3,0,1,1,3,0,4,1,2,1,2,2,8,0,0,0,

%T 7,3,10,1,4,1,2,3,2

%N a(n) is the number of decompositions of 2^(n-1)*(2^n-1) into 3 nonnegative cubes.

%C From _Giovanni Resta_, May 09 2017: (Start)

%C The triples corresponding to n<=40 are reported in the cited paper. Those corresponding to a(41)-a(43) are:

%C 41: (1806336, 90370048, 118874112), (9340200, 89678370, 119250526);

%C 42: (24663948, 61547632, 211219316), (37015132, 42806240, 188598692),

%C     (94126080, 154352128, 172803584);

%C 43: (16384, 266321920, 270516224), (94478388, 245170170, 284820886).

%C (end)

%H Maciej Ulas, <a href="https://arxiv.org/abs/1705.01074">A note on the Diophantine equation 2^(n-1)*(2^n-1)=x^3+y^3+z^3</a>, arXiv:1705.01074 [math.NT], 2017. See Table 1 p. 4.

%t Table[Length@ PowersRepresentations[2^(n - 1) (2^n - 1), 3, 3] - Boole[n == 1], {n, 17}] (* _Michael De Vlieger_, May 08 2017 *)

%Y Cf. A006516, A051343.

%K nonn,more

%O 1,11

%A _Michel Marcus_, May 08 2017

%E a(41)-a(43) from _Giovanni Resta_, May 09 2017