A271331 Rank 2 cluster algebra recurrence with parameters b=4 and c=3 and initial conditions x=2 and y=3.

2, 3, 41, 22974, 6794579902621097, 13653726962325414829845747247532682721242051

Offset

0,1

Comments

This recurrence comes from taking a(0)=2, a(1)=3 with parameters b=4 and c=3 in the well known (rank 2 cluster algebra) recurrence:

a(n) = (1+a(n-1)^b)/a(n-2) if n is even;

a(n) = (1+a(n-1)^c)/a(n-2) if n is odd.

Next term is too large to include.

Links

Table of n, a(n) for n=0..5.

Maple

a:=proc(n) local resp, j; option remember;
if n=0 then return x fi:
if n=1 then return y fi:
   if type(n, even)=true then
      resp:=simplify((1+a(n-1)^b)/a(n-2)):
     else resp:=simplify((1+a(n-1)^c)/a(n-2)):
   fi:
return simplify(resp)
end proc:

Prog

(PARI) a(n) = if (n==0, 2, if (n==1, 3, if (n%2, (1+a(n-1)^3)/a(n-2), (1+a(n-1)^4)/a(n-2)))); \\ Michel Marcus, Apr 04 2016

Crossrefs

Cf. A271330.

Sequence in context: A241277 A123993 A351820 * A101821 A121475 A334533

Adjacent sequences: A271328 A271329 A271330 * A271332 A271333 A271334

Keyword

nonn

Author

Hector J. Blandin N., Apr 04 2016

Status

approved