1,4

Also the number of ways to factor (x^(n^3)-1)/(x-1) into p(x)*q(x)*r(x), such that p(x),q(x),r(x) are polynomials with exactly n terms and all coefficients +1 (and all exponents nonnegative).

a(4)=15 because we can choose any of the following 15 configurations for our three dice: [{0, 1, 2, 3}, {0, 4, 8, 12}, {0, 16, 32, 48}], [{0, 1, 2, 3}, {0, 4, 16, 20}, {0, 8, 32, 40}], [{0, 1, 2, 3}, {0, 4, 32, 36}, {0, 8, 16, 24}], [{0, 1, 4, 5}, {0, 2, 8, 10}, {0, 16, 32, 48}], [{0, 1, 4, 5}, {0, 2, 16, 18}, {0, 8, 32, 40}], [{0, 1, 4, 5}, {0, 2, 32, 34}, {0, 8, 16, 24}], [{0, 1, 8, 9}, {0, 2, 4, 6}, {0, 16, 32, 48}], [{0, 1, 8, 9}, {0, 2, 16, 18}, {0, 4, 32, 36}], [{0, 1, 8, 9}, {0, 2, 32, 34}, {0, 4, 16, 20}], [{0, 1, 16, 17}, {0, 2, 4, 6}, {0, 8, 32, 40}], [{0, 1, 16, 17}, {0, 2, 8, 10}, {0, 4, 32, 36}], [{0, 1, 16, 17}, {0, 2, 32, 34}, {0, 4, 8, 12}], [{0, 1, 32, 33}, {0, 2, 4, 6}, {0, 8, 16, 24}], [{0, 1, 32, 33}, {0, 2, 8, 10}, {0, 4, 16, 20}], [{0, 1, 32, 33}, {0, 2, 16, 18}, {0, 4, 8, 12}]

Sequence in context: A040238 A040239 A126141 this_sequence A049327 A030527 A027467

Adjacent sequences: A131511 A131512 A131513 this_sequence A131515 A131516 A131517

nonn

H.B. Wassenaar (towr(AT)ai.rug.nl), Aug 14 2007