A208223 a(n) = (a(n-1)*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

1, 1, 1, 1, 2, 3, 5, 43, 583, 24306, 386499545, 1781091354996947, 43869039083107828857967559, 104205727286975116465887590166696643681426291537, 1523355234093129576841463666274426784578547247551635338205747270819704358703763325458

Offset: 0

Author

Matthew C. Russell, Apr 25 2012

Keywords

• nonn

Comments

This is the case a=3, b=1, c=1, 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..18
• Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

Crossrefs

Cf. A048736.

Programs

Magma

[n le 4 select 1 else (Self(n-1)*Self(n-3)^3+Self(n-2))/Self(n-4): n in [1..15]]; // Bruno Berselli, Apr 26 2012

Maple

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)*y(n-3)^3+y(n-2))/y(n-4): end:
seq(y(n),n=0..14);

Mathematica

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]a[n-3]^3+a[n-2])/ a[n-4]},a,{n,20}] (* Harvey P. Dale, Jul 13 2014 *)