A096195 a(n) = number of distinct solutions to the set of equations 1 +- x +- x^2 +- ... +- x^n = 0 over the complex numbers.

2, 8, 16, 64, 106, 324, 696, 1856, 4046, 10240, 19084, 49152, 98110, 218140, 464084, 1047744, 2123446, 4718592, 9632740, 20666444

Offset: 1

Author

Josh Locker (jlocker(AT)mail.rochester.edu), Jul 26 2004

Keywords

• more
• nonn

Examples

			a(2) = 8 because the set of equations 1 +- x +- x^2 = 0 generates 8 distinct solutions.
		

Crossrefs

Cf. A036289 (total number of solutions to the equations).

Programs

Mathematica

a[n_] := a[n] = Length[Union[ Flatten[x /. Table[Solve[1 + Sum[(-1)^IntegerDigits[k, 2, n + 1][[p + 1]]x^p, {p, n}] == 0], {k, 0, 2^n - 1}]]]]; Table[a[n], {n, 10}]

Extensions

More terms from Robert G. Wilson v and Labos Elemer, Jul 27 2004

a(17)-a(19) from Robert G. Wilson v, May 05 2013

a(20) from Robert G. Wilson v, May 05 2013