A271331 - OEIS

%I #15 Apr 09 2016 17:20:54

%S 2,3,41,22974,6794579902621097,

%T 13653726962325414829845747247532682721242051

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

%C 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:

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

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

%C Next term is too large to include.

%p a:=proc(n) local resp, j; option remember;

%p if n=0 then return x fi:

%p if n=1 then return y fi:

%p    if type(n,even)=true then

%p       resp:=simplify((1+a(n-1)^b)/a(n-2)):

%p      else resp:=simplify((1+a(n-1)^c)/a(n-2)):

%p    fi:

%p return simplify(resp)

%p end proc:

%o (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

%Y Cf. A271330.

%K nonn

%O 0,1

%A _Hector J. Blandin N._, Apr 04 2016