This site is supported by donations to The OEIS Foundation.

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A262841 Number of irreducible polynomials occurring as the first component of a vertex in the Fibonacci zero tree, generated as in Comments. 3
 0, 0, 1, 2, 3, 5, 8, 11, 21, 28, 54, 68, 135, 183, 360, 470, 948, 1234, 2479, 3294, 6531, 8713, 17120, 23200 (list; graph; refs; listen; history; text; internal format)
 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 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}}}; Do[AppendTo[g, DeleteDuplicates[Partition[Flatten[Join[g, Map[# /. {{0, k_} -> {{0, k + 1}, {k, 0}}, {k_, 0} -> {0, x*k}} &, g]]], 2]]], {z}] t = Table[Drop[g[[k + 1]], Length[g[[k]]]], {k, Length[g] - 1}]; Map[Length, t] (* Fibonacci numbers *) Map[Count[IrreduciblePolynomialQ[#], {_, True}] &, t] (* Peter J. C. Moses, Oct 19 2015 *) CROSSREFS Cf. A000045, A264292. Sequence in context: A177967 A265741 A254351 * A259973 A092362 A105766 Adjacent sequences:  A262838 A262839 A262840 * A262842 A262843 A262844 KEYWORD nonn,easy,more AUTHOR Clark Kimberling, Nov 24 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.