A286351 a(n) is the number of decompositions of 2^(n-1)*(2^n-1) into 3 nonnegative cubes.

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, 7, 3, 10, 1, 4, 1, 2, 3, 2

Offset: 1

Author

Michel Marcus, May 08 2017

Keywords

• nonn
• more

Comments

From Giovanni Resta, May 09 2017: (Start)

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

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

42: (24663948, 61547632, 211219316), (37015132, 42806240, 188598692), (94126080, 154352128, 172803584);

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

(End)

Links

• Maciej Ulas, A note on the Diophantine equation 2^(n-1)*(2^n-1)=x^3+y^3+z^3, arXiv:1705.01074 [math.NT], 2017. See Table 1 p. 4.

Crossrefs

Cf. A006516, A051343.

Programs

Mathematica

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

Extensions

a(41)-a(43) from Giovanni Resta, May 09 2017