OFFSET
0,4
COMMENTS
The tree T is generated by these rules: 0 is in T, and if p is in T, then p + 1 is in T and x*p is in T. Every polynomial with nonnegative integer coefficients is in T, and the n-th generation of T consists of 2^(n-1) polynomials, for n >= 1.
EXAMPLE
First few generations:
g(0) = {0}
g(1) = {1}
g(2) = {2,x}
g(3) = {3, 2x, x+1, x^2}
g(4) = {4, 3x, 2x+1, 2x^2, x+2, x^2+x, x^2+1, x^3}
a(4) counts these 4 irreducible polynomials: 3x, 2x+1, x+2, x^2+1.
MATHEMATICA
z = 15; t = Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {0}, z]];
s[0] = t[[1]]; s[n_] := s[n] = Union[t[[n]], s[n - 1]]
g[n_] := Complement[s[n], s[n - 1]]
Column[Table[g[z], {z, 1, 7}]]
Table[Count[Map[IrreduciblePolynomialQ, g[n]], True], {n, 1, z}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 24 2015
STATUS
approved