This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Table[Floor[(Zeta[3])^n], {n, 1, 100}]
Table[Floor[((1 + Sqrt[3])/2)^n], {n, 1, 100}]
Table[Floor[(Zeta[5])^n], {n, 1, 100}]
Table[Floor[(Pi^2/6)^n], {n, 1, 100}]
[Floor(((1+Sqrt(2))/2)^n): n in [1..100]]; // G. C. Greubel, Oct 02 2018
Table[Floor[((1 + Sqrt[2])/2)^n], {n, 1, 100}]
vector(100, n, floor(((1+sqrt(2))/2)^n)) \\ G. C. Greubel, Oct 02 2018
Table[Floor[((1 + Sqrt[7])/2)^n], {n, 0, 100}]
Quadronacci ratio is root 1.92756... (A086088) of polynomial x^4-x^3-x^2-x-1.
With[{c=x/.FindRoot[x^4-x^3-x^2-x-1==0,{x,1.9}, WorkingPrecision->100]}, Floor[c^Range[40]]] (* Harvey P. Dale, Mar 05 2012 *)