A258169 a(n) = a(n-1)^4/a(n-2) with a(0)=1, a(1)=2.

1, 2, 16, 32768, 72057594037927936, 822752278660603021077484591278675252491367932816789931674304512

Offset: 0

Author

Vaclav Kotesovec, May 22 2015

Keywords

• nonn
• easy

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)).

Crossrefs

Cf. A001353, A112969, A208208, A258161.

Programs

Mathematica

RecurrenceTable[{a[n]==a[n-1]^4/a[n-2], a[0]==1, a[1]==2},a,{n,0,6}]
nxt[{a_,b_}]:={b,b^4/a}; NestList[nxt,{1,2},5][[All,1]] (* Harvey P. Dale, Sep 04 2022 *)

Formula

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

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