OFFSET
0,4
COMMENTS
An example where the degree of the n-th iterate of a rational map exhibits polynomial growth. Also an example for exponential growth was given in the thesis from Khaled Hamad by A011782.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000
Khaled Hamad, Laurentification, Thesis (2017). La Trobe University.
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,-2,1).
FORMULA
G.f.: (1 - x + x^3 + x^4 - x^5 + x^6 + x^8)/(1 - 2*x + x^2 - x^7 + 2*x^8 - x^9).
a(n) = ceiling((3*n^2 - 3*n + 8)/14).
a(n) = 2*a(n-1) - a(n-2) + a(n-7) - 2*a(n-8) + a(n-9).
a(n) = a(n-7) + 3*(n-7) + 9.
(2*a(n+6) - a(n+5) - 2*a(n-1) + a(n-2) - 9)/3 = n.
MATHEMATICA
A376080[n_] := Ceiling[(3*n*(n - 1) + 8)/14];
Array[A376080, 100, 0] (* Paolo Xausa, Sep 23 2024 *)
PROG
(PARI)
r(v) = [v[2], (v[2]+1)/(v[1]*v[2])];
a(n) = {my(v = [x, x]); if(n < 2, 1, for(k=0, n-2, v = r(v)); poldegree(numerator(v[2])))};
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thomas Scheuerle, Sep 09 2024
STATUS
approved