The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007759 Knopfmacher expansion of sqrt(2): a(2n) = 2*(a(2n-1) + 1)^2 - 1, a(2n+1) = 2*(a(2n)^2 - 1). 2
 2, 17, 576, 665857, 886731088896, 1572584048032918633353217, 4946041176255201878775086487573351061418968498176, 48926646634423881954586808839856694558492182258668537145547700898547222910968507268117381704646657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..11 A. Knopfmacher and J. Knopfmacher, An alternating product representation for real numbers, in Applications of Fibonacci numbers, Vol. 3 (Kluwer 1990), pp. 209-216. MAPLE a:= proc(n) option remember; if n=1 then 2 elif `mod`(n, 2) = 0 then 2*(a(n-1) +1)^2 -1 else 2*(a(n-1)^2 -1) end if; end proc; seq(a(n), n = 1..9); # G. C. Greubel, Mar 04 2020 MATHEMATICA a[n_]:= a[n]= If[n==1, 2, If[EvenQ[n], 2*(a[n-1] +1)^2 -1, 2*a[n-1]^2 -2]]; Table[a[n], {n, 9}] (* G. C. Greubel, Mar 04 2020 *) PROG (PARI) a(n) = if (n==1, 2, if (n % 2, 2*a(n-1)^2 - 2, 2*(a(n-1)+1)^2 - 1)); \\ Michel Marcus, Feb 20 2019 (Magma) function a(n) if n eq 1 then return 2; elif n mod 2 eq 0 then return 2*(a(n-1) +1)^2 -1; else return 2*(a(n-1)^2 -1); end if; return a; end function; [a(n): n in [1..9]]; // G. C. Greubel, Mar 04 2020 (Sage) @CachedFunction def a(n): if (n==1): return 2 elif (n%2==0): return 2*(a(n-1) +1)^2 -1 else: return 2*(a(n-1)^2 -1) [a(n) for n in (1..9)] # G. C. Greubel, Mar 04 2020 CROSSREFS Cf. A002193 (sqrt(2)), A001601. Sequence in context: A293178 A172341 A356502 * A062710 A012939 A013094 Adjacent sequences: A007756 A007757 A007758 * A007760 A007761 A007762 KEYWORD nonn AUTHOR Arnold Knopfmacher EXTENSIONS More terms from Christian G. Bower, Jan 06 2006 STATUS approved

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

Last modified November 29 20:40 EST 2023. Contains 367447 sequences. (Running on oeis4.)