A208221 -id:A208221 - cp's OEIS frontend

A208222 a(n) = (a(n-1)^3*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

1, 1, 1, 1, 2, 9, 731, 1562471573, 154486807085783774292345385804

Offset: 0

Matthew C. Russell, Apr 25 2012

nonn

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).

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.

Cf. A048736, A208219, A208221, A208225.

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);

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 *)

A208224 a(n)=(a(n-1)^2*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

Original entry on oeis.org

1, 1, 1, 1, 2, 5, 27, 5837, 2129410576, 17850077316687753782569, 2346851008195218976646246398770505953580095510848345967

Offset: 0

Matthew C. Russell, Apr 25 2012

nonn

This is the case a=3, b=1, c=2, 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).

The next term (a(11)) has 133 digits. - Harvey P. Dale, Mar 06 2017

Seiichi Manyama, Table of n, a(n) for n = 0..13
Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

Cf. A048736, A208221, A208223, A208225, A208227.

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^2*y(n-3)^3+y(n-2))/y(n-4): end:
seq(y(n),n=0..11);

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]^2*a[n-3]^3+ a[n-2])/ a[n-4]},a,{n,10}] (* Harvey P. Dale, Mar 06 2017 *)

cp's OEIS Frontend

A208222 a(n) = (a(n-1)^3*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

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