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.
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
KEYWORD
nonn
AUTHOR
Hector J. Blandin N., Apr 04 2016
STATUS
approved