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A182229 a(n) = a(n-1) + floor(a(n-2)/3) with a(0)=2, a(1)=3.

%I A182229 #21 Sep 08 2022 08:45:55
%S A182229 2,3,3,4,5,6,7,9,11,14,17,21,26,33,41,52,65,82,103,130,164,207,261,
%T A182229 330,417,527,666,841,1063,1343,1697,2144,2709,3423,4326,5467,6909,
%U A182229 8731,11034,13944,17622,22270,28144,35567,44948,56803,71785,90719,114647,144886,183101
%N A182229 a(n) = a(n-1) + floor(a(n-2)/3) with a(0)=2, a(1)=3.
%C A182229 a(n)/a(n-1) tends to (3+sqrt(21))/6 = 1.263762615825973334... [_Bruno Berselli_, Apr 23 2012]
%H A182229 Bruno Berselli, <a href="/A182229/b182229.txt">Table of n, a(n) for n = 0..1000</a>
%t A182229 RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == a[n - 1] + Floor[a[n - 2]/3]}, a, {n, 50}] (* _Bruno Berselli_, Apr 21 2012 *)
%o A182229 (Python)
%o A182229 prpr = 2
%o A182229 prev = 3
%o A182229 for i in range(2,51):
%o A182229     current = prev + prpr//3
%o A182229     print(current, end=',')
%o A182229     prpr = prev
%o A182229     prev = current
%o A182229 (Magma) [n le 2 select n+1 else Self(n-1)+Floor(Self(n-2)/3): n in [1..51]]; // _Bruno Berselli_, Apr 21 2012
%o A182229 (Haskell)
%o A182229 a182229 n = a182229_list !! n
%o A182229 a182229_list = 2 : 3 : zipWith (+)
%o A182229                        (map (flip div 3) a182229_list) (tail a182229_list)
%o A182229 -- _Reinhard Zumkeller_, Apr 30 2015
%Y A182229 Cf. A064324, A182281, A182230; A176014.
%K A182229 nonn
%O A182229 0,1
%A A182229 _Alex Ratushnyak_, Apr 19 2012