OFFSET
0,2
REFERENCES
Archimedeans Problems Drive, Eureka, 19 (1957), 13.
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
T. D. Noe, Table of n, a(n) for n = 0..17
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link.
FORMULA
a(n) ~ c^(phi^n), where c = A258112 = 1.7978784900091604813559508837..., phi = (1+sqrt(5))/2 = A001622. - Vaclav Kotesovec, Dec 17 2014
MAPLE
a:= proc (n) option remember;
if n=0 then 1
elif n=1 then 3
else a(n-1)*a(n-2) + 1
end if
end proc;
seq(a(n), n = 0..13); # G. C. Greubel, Sep 19 2019
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==3, a[n]==a[n-1]*a[n-2]+1}, a, {n, 0, 14}] (* Harvey P. Dale, Jul 17 2011 *)
t = {1, 3}; Do[AppendTo[t, t[[-1]] * t[[-2]] + 1], {n, 2, 14}] (* T. D. Noe, Jun 25 2012 *)
PROG
(Haskell)
a001056 n = a001056_list !! n
a001056_list = 1 : 3 : (map (+ 1 ) $
zipWith (*) a001056_list $ tail a001056_list)
-- Reinhard Zumkeller, Aug 15 2012
(PARI) m=13; v=concat([1, 3], vector(m-2)); for(n=3, m, v[n]=v[n-1]*v[n-2] +1 ); v \\ G. C. Greubel, Sep 19 2019
(Magma) I:=[1, 3]; [n le 2 select I[n] else Self(n-1)*Self(n-2) + 1: n in [1..13]]; // G. C. Greubel, Sep 19 2019
(Sage)
def a(n):
if (n==0): return 1
elif (n==1): return 3
else: return a(n-1)*a(n-2) + 1
[a(n) for n in (0..13)] # G. C. Greubel, Sep 19 2019
(GAP) a:=[1, 3];; for n in [3..13] do a[n]:=a[n-1]*a[n-2]+1; od; a; # G. C. Greubel, Sep 19 2019
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved