OFFSET
0,5
COMMENTS
This is the case a=2, b=1, c=3, y(0)=y(1)=y(2)=y(3)=1 of the recurrence shown in the Example 3.3 of "The Laurent phenomenon" (see Link lines, p. 10).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..11
Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.
MAPLE
y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^3*y(n-3)^2+y(n-2))/y(n-4): end:
seq(y(n), n=0..9);
MATHEMATICA
a[n_]:=If[n<4, 1, (a[n - 1]^3*a[n - 3]^2 + a[n - 2])/a[n - 4]]; Table[a[n], {n, 0, 11}] (* Indranil Ghosh, Mar 19 2017 *)
nxt[{a_, b_, c_, d_}]:={b, c, d, (d^3 b^2+c)/a}; NestList[nxt, {1, 1, 1, 1}, 10][[All, 1]] (* Harvey P. Dale, May 31 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew C. Russell, Apr 25 2012
STATUS
approved