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a(n) = 7 + floor(Sum_{j=1..n-1} a(j) / 2).
3

%I #14 May 13 2023 19:20:20

%S 7,10,15,23,34,51,77,115,173,259,389,583,875,1312,1968,2952,4428,6642,

%T 9963,14945,22417,33626,50439,75658,113487,170231,255346,383019,

%U 574529,861793,1292690,1939035,2908552,4362828,6544242,9816363,14724545

%N a(n) = 7 + floor(Sum_{j=1..n-1} a(j) / 2).

%H Harvey P. Dale, <a href="/A120136/b120136.txt">Table of n, a(n) for n = 1..1000</a>

%t nxt[{t_,a_}] := Module[{c=7+Floor[t/2]},{t+c,c}];

%t NestList[nxt,{7,7},40][[All,2]] (* _Harvey P. Dale_, Jan 13 2017 *)

%o (SageMath)

%o @CachedFunction

%o def A120136(n): return 7 +sum(A120136(k) for k in range(1,n))//2

%o [A120136(n) for n in range(1,60)] # _G. C. Greubel_, May 08 2023

%Y Cf. A073941, A072493, A112088, A120134, A120135, A120137 - A120209.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006