OFFSET
0,13
COMMENTS
Limiting ratio is:1.0754819626288792.
The integer 5 in the Fibonacci Binet formula is replaced by the minimal Pisot real root as a beta integer to design a very low ratio sequence.
FORMULA
a0=1.324717957244746;
alpha=1.0754819626288792;
beta=-0.07548196262887907;
a(n)=Floor[(alpha^n-beta^n)/(alpha-beta)]
MATHEMATICA
a0 = x /. NSolve[x^3 - x - 1 == 0, x][[3]]
a = (1 + Sqrt[a0])/2; b = (1 - Sqrt[a0])/2;
f[n_] := Floor[FullSimplify[(a^n - b^n)/(a - b)]]
Table[f[n], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 29 2010
STATUS
approved