The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001056 a(n) = a(n-1)*a(n-2) + 1, a(0) = 1, a(1) = 3. (Formerly M2378 N0944) 3
 1, 3, 4, 13, 53, 690, 36571, 25233991, 922832284862, 23286741570717144243, 21489756930695820973683319349467, 500426416062641238759467086706254193219790764168482, 10754042042885415070816603338436200915110904821126871858491675028294447933424899095 (list; graph; refs; listen; history; text; internal format)
 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, Fib. Quart., 11 (1973), 429-437. 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 Cf. A001622 (phi), A258112. Sequence in context: A062165 A243764 A201821 * A122151 A294384 A216868 Adjacent sequences:  A001053 A001054 A001055 * A001057 A001058 A001059 KEYWORD nonn,easy,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)