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A120151 a(n) = 5 + floor( Sum_{j=1..n-1} a(j)/3 ).

%I A120151 #10 Jun 16 2023 08:11:16
%S A120151 5,6,8,11,15,20,26,35,47,62,83,111,148,197,263,350,467,623,830,1107,
%T A120151 1476,1968,2624,3499,4665,6220,8293,11058,14744,19658,26211,34948,
%U A120151 46597,62130,82840,110453,147271,196361,261815,349086,465448,620598,827464,1103285
%N A120151 a(n) = 5 + floor( Sum_{j=1..n-1} a(j)/3 ).
%H A120151 Harvey P. Dale, <a href="/A120151/b120151.txt">Table of n, a(n) for n = 1..1000</a>
%p A120151 a:= proc(n) option remember;
%p A120151        5+floor(add(a(j)/3, j=1..n-1))
%p A120151     end:
%p A120151 seq(a(n), n=1..44);  # _Alois P. Heinz_, Jun 16 2023
%t A120151 nxt[{t_,n_}]:=Module[{c=Floor[(15+t)/3]},{t+c,c}]; NestList[nxt,{5,5},40][[All,2]] (* _Harvey P. Dale_, Jun 19 2022 *)
%o A120151 (Magma)
%o A120151 function f(n,a,b)
%o A120151   t:=0;
%o A120151     for k in [1..n-1] do
%o A120151        t+:= a+Floor((b+t)/3);
%o A120151      end for;
%o A120151   return t;
%o A120151 end function;
%o A120151 g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
%o A120151 A120151:= func< n | g(n,5,0) >;
%o A120151 [A120151(n): n in [1..60]]; // _G. C. Greubel_, Jun 15 2023
%o A120151 (SageMath)
%o A120151 @CachedFunction
%o A120151 def A120151(n): return 5 + (sum(A120151(k) for k in range(1, n)))//3
%o A120151 [A120151(n) for n in range(1, 61)] # _G. C. Greubel_, Jun 15 2023
%Y A120151 Cf. A072493, A073941, A112088.
%K A120151 nonn
%O A120151 1,1
%A A120151 _Graeme McRae_, Jun 10 2006