A093333 - OEIS

%I #24 Feb 01 2025 16:55:13

%S 0,1,1,2,2,4,5,8,12,19,30,47,75,118,188,297,472,748,1188,1885,2992,

%T 4749,7538,11966,18994,30151,47861,75975,120602,191444,303898,482408,

%U 765774,1215591,1929629,3063096,4862361,7718517,12252381,19449443,30874065

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

%H Harvey P. Dale, <a href="/A093333/b093333.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = c*2^(2n/3)+O(1) where c = 0.4600594211686036392470119450103830526110335102224661416117198000.... - _Benoit Cloitre_, Dec 17 2006

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

%t 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 *)

%t nxt[{a_,b_}]:={b,Floor[2*Sqrt[a*b]]}; Join[{0},NestList[nxt,{1,1},40][[;;,1]]] (* _Harvey P. Dale_, Feb 01 2025 *)

%Y Cf. A093332, A093335.

%K easy,nonn

%O 0,4

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