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A271330 Rank 2 cluster algebra recurrence with parameters b=c=3 and initial conditions a(0)=2 and a(1)=3. 1
2, 3, 14, 915, 54718634, 179054255520688074387, 104910436622395373760090792140594526518830577847960206 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This recurrence comes from taking a(0)=2, a(1)=3 with parameters b=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.

LINKS

Table of n, a(n) for n=0..6.

FORMULA

a(n) = (1+a(n-1)^3)/a(n-2), n>=2,  a(0)=2, a(1)=3.

a(n) ~ c^(((1+sqrt(5))/2)^(2*n)), where c = 1.46103748126346957816556... . - Vaclav Kotesovec, Apr 08 2016

MAPLE

# Here we set x=a(0) and y=a(1) to be appropriate initial conditions to produce an integer sequence.

# In general we do not obtain an integer sequence.

# The values x=2, y=3 are appropriate initial conditions when b=c=3.

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:

MATHEMATICA

a[0] = 2; a[1] = 3; a[n_] := a[n] = (1 + a[n - 1]^3)/a[n - 2]; Array[a, 8, 0] (* Michael De Vlieger, Apr 08 2016 *)

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)^3)/a(n-2)))); \\ Michel Marcus, Apr 04 2016

CROSSREFS

Cf. A271331.

Sequence in context: A042071 A042817 A224848 * A262462 A180698 A266618

Adjacent sequences:  A271327 A271328 A271329 * A271331 A271332 A271333

KEYWORD

nonn

AUTHOR

Hector J. Blandin N., Apr 04 2016

STATUS

approved

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Last modified June 5 09:58 EDT 2020. Contains 334840 sequences. (Running on oeis4.)