OFFSET
1,2
COMMENTS
R is the so-called plastic number (A060006). Padovan(n) = (r^n)/(2r+3) + (s^n)/(2s+3) + (t^n)/(2t+3) where r (real), s, t are the three roots of x^3-x-1. Also Padovan(n) is asymptotic to r^n / (2*r+3).
EXAMPLE
For n=25, Padovan(25) = A000931(25) = 200 < 200.023... = r^25/(2*r+3).
MATHEMATICA
lim=200; R = Solve[x^3 - x - 1 == 0, x][[1, 1, 2]]; powers = Table[Floor[R^n/(2*R + 3)], {n, lim}]; p = Rest[CoefficientList[Series[(1 - x^2)/(1 - x^2 - x^3), {x, 0, lim}], x]]; Select[Range[lim], p[[#]] <= powers[[#]] &] (* T. D. Noe, Aug 01 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Francesco Daddi, Jul 31 2011
STATUS
approved