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a(1)=5; a(n)=floor((39+sum(a(1) to a(n-1)))/7).
1

%I #6 Sep 13 2020 11:50:21

%S 5,6,7,8,9,10,12,13,15,17,20,23,26,30,34,39,44,51,58,66,76,86,99,113,

%T 129,147,168,192,220,251,287,328,375,429,490,560,640,731,836,955

%N a(1)=5; a(n)=floor((39+sum(a(1) to a(n-1)))/7).

%H Harvey P. Dale, <a href="/A120190/b120190.txt">Table of n, a(n) for n = 1..1000</a>

%t nxt[{s_,a_}]:=Module[{c=Floor[(39+s)/7]},{s+c,c}]; NestList[nxt,{5,5},40][[All,2]] (* _Harvey P. Dale_, Sep 13 2020 *)

%Y Cf. A073941, A112088, A072493.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006