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A007759
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Knopfmacher expansion of sqrt(2): a(2n) = 2*(a(2n-1) + 1)^2 - 1, a(2n+1) = 2*(a(2n)^2 - 1).
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2
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2, 17, 576, 665857, 886731088896, 1572584048032918633353217, 4946041176255201878775086487573351061418968498176, 48926646634423881954586808839856694558492182258668537145547700898547222910968507268117381704646657
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OFFSET
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1,1
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LINKS
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MAPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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(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;
(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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