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A024551
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a(n) = floor(a(n-1)/(sqrt(5) - 2)) for n > 0 and a(0) = 1.
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4
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1, 4, 16, 67, 283, 1198, 5074, 21493, 91045, 385672, 1633732, 6920599, 29316127, 124185106, 526056550, 2228411305, 9439701769, 39987218380, 169388575288, 717541519531, 3039554653411, 12875760133174, 54542595186106, 231046140877597
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (-x^2-x+1)/[(1-x)(1-4x-x^2)].
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MATHEMATICA
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a[0] = 1;
a[n_] := Floor[a[n - 1]/FractionalPart[Sqrt[5]]]
Table[a[n], {n, 0, 60}]
a[0]=1;
a[1]=4;
a[2]=16;
a[n_]:=Floor[a[n-1]^2/a[n-2]]+3
Table[a[n], {n, 0, 60}]
With[{c=Sqrt[5]-2}, NestList[Floor[#/c]&, 1, 30]] (* Harvey P. Dale, Jul 18 2018 *)
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PROG
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(PARI) step(n)=2*n + sqrtint(5*n^2)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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