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A258169 a(n) = a(n-1)^4/a(n-2) with a(0)=1, a(1)=2. 1
1, 2, 16, 32768, 72057594037927936, 822752278660603021077484591278675252491367932816789931674304512 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The next term has 235 digits.

In general, the recurrence a(n) = a(n-1)^k / a(n-2) with a(0) = 1, a(1) = m, k > 2, has a solution a(n) = m^(((k+sqrt(k^2-4))^n - (k-sqrt(k^2-4))^n) / (sqrt(k^2-4) * 2^n)).

LINKS

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

FORMULA

a(n) = 2^(A001353(n)).

a(n) = 2^(((2+sqrt(3))^n-(2-sqrt(3))^n)/(2*sqrt(3))).

MATHEMATICA

RecurrenceTable[{a[n]==a[n-1]^4/a[n-2], a[0]==1, a[1]==2}, a, {n, 0, 6}]

CROSSREFS

Cf. A001353, A112969, A208208, A258161.

Sequence in context: A306729 A325049 A092798 * A325048 A068916 A093987

Adjacent sequences:  A258166 A258167 A258168 * A258170 A258171 A258172

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 22 2015

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)