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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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified December 11 04:29 EST 2018. Contains 318049 sequences. (Running on oeis4.)