A208219 a(n)=(a(n-1)^3*a(n-3)+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

1, 1, 1, 1, 2, 9, 731, 781235791, 2145650135491172007486084385, 802327342392981520933850619811649523436811893002103478524225246677189521545661182074

Offset

0,5

Comments

This is the case a=1, 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).

The next term (a(10)) has 258 digits. - Harvey P. Dale, Sep 21 2016

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)+y(n-2))/y(n-4): end:
seq(y(n), n=0..9);

Mathematica

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1, a[n]==(a[n-1]^3 a[n-3]+ a[n-2])/ a[n-4]}, a, {n, 10}] (* Harvey P. Dale, Sep 21 2016 *)

Crossrefs

Cf. A048736, A208218, A208222.

Sequence in context: A135361 A023366 A000284 * A208222 A208225 A208228

Adjacent sequences: A208216 A208217 A208218 * A208220 A208221 A208222

Keyword

nonn

Author

Matthew C. Russell, Apr 25 2012

Status

approved