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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
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-François 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
Sequence in context: A057438 A002795 A208218 * A208224 A208227 A127357
KEYWORD
nonn
AUTHOR
Matthew C. Russell, Apr 25 2012
STATUS
approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)