

A264292


Number of irreducible polynomials in the polynomial tree T generated as in Comments.


2



0, 0, 1, 2, 4, 7, 15, 26, 55, 101, 221, 413, 870, 1673, 3490
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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 nth generation of T consists of 2^(n1) polynomials, for n >= 1.


LINKS

Table of n, a(n) for n=0..14.


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

Cf. A000072, A262841.
Sequence in context: A027167 A259090 A232464 * A259592 A291220 A299099
Adjacent sequences: A264289 A264290 A264291 * A264293 A264294 A264295


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Nov 24 2015


STATUS

approved



