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

0, 2, 8, 16, 64, 106, 324, 696, 1856, 4046, 10240, 19084, 49152, 98110, 218140, 464084, 1047744, 2123446, 4718592, 9632740, 20666444, 43283582, 92271828, 186979328, 401822544, 828214466, 1733156480, 3567782988, 7516192768

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

For n in A071642, a(n) = n * 2^n. - Max Alekseyev, Nov 07 2025

Example

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

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}]

Crossrefs

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

Sequence in context: A100243 A026523 A066792 * A094014 A098232 A354275

Adjacent sequences: A096192 A096193 A096194 * A096196 A096197 A096198

Keyword

nonn

Author

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

Extensions

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

a(17)-a(20) from Robert G. Wilson v, May 05 2013

a(0) prepended, a(21)-a(28) added by Max Alekseyev, Nov 06 2025

Status

approved