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A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.

%I A173497 #18 Aug 30 2020 22:15:41
%S A173497 2,1,2,3,4,6,8,11,15,21,29,40,55,75,103,141,193,264,361,493,674,921,
%T A173497 1258,1719,2348,3208,4382,5986,8177,11170,15259,20844,28474,38896,
%U A173497 53133,72581,99148,135439,185013,252733,345240,471607,644227,880031
%N A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.
%C A173497 The limiting ratio is a(n+1)/a(n): 1.36602540378443.
%C A173497 This limiting ratio is (1+sqrt(3))/2. - _Robert Israel_, Aug 30 2020
%H A173497 Robert Israel, <a href="/A173497/b173497.txt">Table of n, a(n) for n = 0..7374</a>
%F A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2).
%p A173497 A[0]:= 2: A[1]:= 1:
%p A173497 for n from 2 to 100 do
%p A173497   A[n]:= A[n-1]+A[n-2]-floor(A[n-2]/2)
%p A173497 od:
%p A173497 seq(A[i],i=0..100); # _Robert Israel_, Aug 30 2020
%t A173497 l[0] = 2; l[1] = 1;
%t A173497 l[n_] := l[n] = l[n - 1] + l[n - 2] - Floor[l[n - 2]/2]
%t A173497 Table[l[n], {n, 0, 30}]
%t A173497 RecurrenceTable[{a[0]==2,a[1]==1,a[n]==a[n-1]+a[n-2]-Floor[a[n-2]/2]},a,{n,50}] (* _Harvey P. Dale_, Apr 26 2016 *)
%Y A173497 Cf. A064323, A000032.
%K A173497 nonn
%O A173497 0,1
%A A173497 _Roger L. Bagula_, Nov 23 2010
%E A173497 More terms from _Max Alekseyev_, Jun 18 2011