OFFSET
0,5
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..16
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!)
FORMULA
a(n)^2 = a(n+1) + a(n-1), a(-1-n) = a(n).
For n >= 4, a(n) = ceiling(c^(2^n)) with c=1.0303497388742578142745024606710866\
16436302563960998408889321488508667424048981473368773165340730475719244472111...
and c^(1/4) = 1.0075025785879710605024343257517358... - Benoit Cloitre, Apr 16 2007
EXAMPLE
a(6) = a(5)^2 - a(4) = 3^2 - 2 = 7.
MATHEMATICA
Join[{a=1, b=0}, Table[c=b^2-a; a=b; b=c, {n, 13}]] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2011 *)
RecurrenceTable[{a[0]==1, a[1]==0, a[n]==a[n-1]^2 - a[n-2]}, a, {n, 13}] (* Vincenzo Librandi, Nov 11 2012 *)
PROG
(PARI) a(n)=if(n<0, a(-1-n), if(n<2, 1-n, a(n-1)^2-a(n-2))) /* Michael Somos, May 05 2005 */
(Magma) I:=[1, 0]; [n le 2 select I[n] else Self(n-1)^2 - Self(n-2): n in [1..15]]; // G. C. Greubel, Jun 09 2019
(Sage)
def a(n):
if (n==0): return 1
elif (n==1): return 0
else: return a(n-1)^2 - a(n-2)
[a(n) for n in (0..15)] # G. C. Greubel, Jun 09 2019
(GAP) a:=[1, 0];; for n in [3..15] do a[n]:=a[n-1]^2-a[n-2]; od; a; # G. C. Greubel, Jun 09 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Henry Bottomley, Nov 15 2000
STATUS
approved