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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 September 19 18:07 EDT 2024. Contains 376014 sequences. (Running on oeis4.)