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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 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 = t[]; 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. A000079, 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 May 16 14:48 EDT 2022. Contains 353704 sequences. (Running on oeis4.)