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A208221 a(n)=(a(n-1)^2*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1. 3
1, 1, 1, 1, 2, 5, 27, 2921, 106653026, 1658455747832683945, 869174798276372512100586962107665002957113 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

This is the case a=2, 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 97 digits. - Harvey P. Dale, Dec 17 2017

LINKS

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.

MAPLE

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^2*y(n-3)^2+y(n-2))/y(n-4): end:

seq(y(n), n=0..11);

MATHEMATICA

a[n_] := a[n] = If[n <= 3, 1, (a[n-1]^2*a[n-3]^2 + a[n-2])/a[n-4]];

Table[a[n], {n, 0, 13}] (* Jean-Fran├žois Alcover, Nov 24 2017 *)

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1, a[n]==(a[n-1]^2 a[n-3]^2+ a[n-2])/ a[n-4]}, a, {n, 12}] (* Harvey P. Dale, Dec 17 2017 *)

CROSSREFS

Cf. A048736, A208218, A208220, A208222, A208224.

Sequence in context: A057438 A002795 A208218 * A208224 A208227 A127357

Adjacent sequences:  A208218 A208219 A208220 * A208222 A208223 A208224

KEYWORD

nonn

AUTHOR

Matthew C. Russell, Apr 25 2012

STATUS

approved

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Last modified August 6 11:55 EDT 2020. Contains 336246 sequences. (Running on oeis4.)