A001042 a(n) = a(n-1)^2 - a(n-2)^2.
1, 2, 3, 5, 16, 231, 53105, 2820087664, 7952894429824835871, 63248529811938901240357985099443351745, 4000376523371723941902615329287219027543200136435757892789536976747706216384
Offset: 0
References
- Archimedeans Problems Drive, Eureka, 27 (1964), 6.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..13
- A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
- A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
- R. K. Guy, Letters to N. J. A. Sloane, June-August 1968
- R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.
- Index entries for sequences of form a(n+1)=a(n)^2 + ...
Programs
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Haskell
a001042 n = a001042_list !! n a001042_list = 1 : 2 : zipWith (-) (tail xs) xs where xs = map (^ 2) a001042_list -- Reinhard Zumkeller, Dec 16 2013 -
Mathematica
RecurrenceTable[{a[0]==1,a[1]==2,a[n]==a[n-1]^2-a[n-2]^2},a,{n,0,12}] (* Harvey P. Dale, Jan 11 2013 *)
Formula
a(n) ~ c^(2^n), where c = 1.1853051643868354640833201434870139866230288004895868726506278977814490371... . - Vaclav Kotesovec, Dec 17 2014
Extensions
More terms from James Sellers, Sep 19 2000.
Comments