A093333 a(0) = 0, a(1) = 1 and for n >= 2, a(n) = floor(2 * sqrt(a(n-2) * a(n-1))).

0, 1, 1, 2, 2, 4, 5, 8, 12, 19, 30, 47, 75, 118, 188, 297, 472, 748, 1188, 1885, 2992, 4749, 7538, 11966, 18994, 30151, 47861, 75975, 120602, 191444, 303898, 482408, 765774, 1215591, 1929629, 3063096, 4862361, 7718517, 12252381, 19449443, 30874065

Offset

0,4

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n) = c*2^(2n/3)+O(1) where c = 0.4600594211686036392470119450103830526110335102224661416117198000.... - Benoit Cloitre, Dec 17 2006

Example

a(5) = 4 because a(5) = floor(2*sqrt(a(3)*a(4))) = floor(2*sqrt(2*2)) = 4.

Mathematica

Join[{0}, RecurrenceTable[{a[1]==a[2]==1, a[n]==Floor[2Sqrt[a[n-1]a[n-2]]]}, a, {n, 40}]] (* Harvey P. Dale, Jun 14 2014 *)
nxt[{a_, b_}]:={b, Floor[2*Sqrt[a*b]]}; Join[{0}, NestList[nxt, {1, 1}, 40][[;; , 1]]] (* Harvey P. Dale, Feb 01 2025 *)

Crossrefs

Cf. A093332, A093335.

Sequence in context: A274153 A079501 A093335 * A116085 A329692 A216198

Adjacent sequences: A093330 A093331 A093332 * A093334 A093335 A093336

Keyword

easy,nonn

Author

Robert A. Stump (rstump_2004(AT)yahoo.com), Apr 25 2004

Status

approved