Records of number of terms of polynomial subsequencces.
  [2nd degree]
  { x0, p, a, b = 2443499297,2,2.00014,3.0 }
  68 terms , 0-th > 67-th
  x(n) = 6*n^2+171040*n+2443499297
  
  [3rd degre]
  { x0, p, a, b = 2417903893829791,2,2.00013,3.0 }
  5 terms , 0-th > 4-th
  x(n) = 664/6*n^3+5107490*n^2+471475936498/3*n+2417903893829791
 
  [4th degree]
  { x0, p, a, b = 2015985557869547951,2,2.00013,3.2 }
  8 terms , 0-th > 7-th
 
 
  I appreciate for receiving any update of higher degree than 2nd and more terms than each records.
  Please mail to :   zbi74583@boat.zero.ad.jp
 
  I also conjectured as follows :
  "LLI which has exponecial subsequences and LLI which has Fibonatti subsequences exist."
  Search them !!