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A064650 a(n) = floor(a(n-1)/2) + a(n-2) with a(0)=1, a(1)=2.

%I A064650 #22 Sep 08 2022 08:45:04
%S A064650 1,2,2,3,3,4,5,6,8,10,13,16,21,26,34,43,55,70,90,115,147,188,241,308,
%T A064650 395,505,647,828,1061,1358,1740,2228,2854,3655,4681,5995,7678,9834,
%U A064650 12595,16131,20660,26461,33890,43406,55593,71202,91194,116799,149593,191595
%N A064650 a(n) = floor(a(n-1)/2) + a(n-2) with a(0)=1, a(1)=2.
%C A064650 a(n)/a(n-1) tends to (1+sqrt(17))/4 = 1.2807764...
%H A064650 Harry J. Smith and Reinhard Zumkeller, <a href="/A064650/b064650.txt">Table of n, a(n) for n = 0..9300</a>, first 401 terms from Harry J. Smith
%F A064650 a(n) = A064651(n) + 1.
%t A064650 RecurrenceTable[{a[0] == 1, a[1] == 2, a[n] == Floor[a[n - 1]/4] + a[n - 2]}, a, {n, 49}] (* _Bruno Berselli_, Apr 21 2012 *)
%o A064650 (PARI) { for (n=0, 400, if (n>1, a=a1\2 + a2; a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b064650.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 21 2009
%o A064650 (Magma) [n le 2 select n else Floor(Self(n-1)/2)+Self(n-2): n in [1..50]]; // _Bruno Berselli_, Apr 21 2012
%o A064650 (Haskell)
%o A064650 a064650 n = a064650_list !! n
%o A064650 a064650_list = 1 : 2 : zipWith (+)
%o A064650                        a064650_list (map (flip div 2) $ tail a064650_list)
%o A064650 -- _Reinhard Zumkeller_, Apr 30 2015
%Y A064650 Cf. A064324, A064325, A182280, A182281.
%Y A064650 Cf. A064651, A000045.
%K A064650 nonn
%O A064650 0,2
%A A064650 _Henry Bottomley_, Oct 04 2001