A262841 - OEIS

A262841

Number of irreducible polynomials occurring as the first component of a vertex in the Fibonacci zero tree, generated as in Comments.

0, 0, 1, 2, 3, 5, 8, 11, 21, 28, 54, 68, 135, 183, 360, 470, 948, 1234, 2479, 3294, 6531, 8713, 17120, 23200

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OFFSET

0,4

COMMENTS

The tree T, which we call the Fibonacci zero tree, is generated by these rules: (0, 0) is in T, and if (0, h) is in T, then (0, h + 1) is in T, and if (k, 0) is in T, then (0, k*x) is in T. The number of vertices (f(x),g(x)) in the n-th generation of T is F(n+1), where F = A000045, the Fibonacci numbers, for n >= 0.

The number of irreducible polynomials occurring as the second component of a vertex in the tree T is a(n-1) for n >= 1.

LINKS

Table of n, a(n) for n=0..23.

EXAMPLE

First few generations:

g(0) = {(0,0)}

g(1) = {(0,2), (1,0)}

g(2) = {(0,3), (2,0), (0,x)}

g(3) = {(0,4), (3,0), (0,2x), (0,1+x), (x,0)}

g(4) = {(0,5), (4,0), (0,3x), (0,1+2x), (2x,0), (0,2+x), (1+x,0), (0,x^2)}

MATHEMATICA

z = 20; g = {{{0, 0}}};