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%I #11 Nov 15 2024 17:40:42
%S 1,3,4,5,3,2,2,3,4,5,5,4,3,3,4,5,6,5,5,4,5,5,6,5,6,5,6,5,6,5,7,6,7,5,
%T 6,5,8,7,9,6,7,5,7,7,9,7,7,6,7,7,9,8,8,7,7,7,8,9,9,8,7,7,8,9,10,9,8,7,
%U 8,9,11,10,9,7,8,9,11,10,10,8,9,9,11,10
%N a(n) = floor((a(n-1)+a(n-2)+n)/(a(n-3)+1)), with a(1)=1, a(2)=3, a(3)=4.
%H Harvey P. Dale, <a href="/A372984/b372984.txt">Table of n, a(n) for n = 1..1000</a>
%t a[1] = 1; a[2] = 3; a[3] = 4;
%t a[n_] := a[n] = Floor[(a[n - 1] + a[n - 2] + n)/(a[n - 3] + 1)];
%t Table[a[n], {n, 1, 100}]
%t nxt[{n_,a_,b_,c_}]:={n+1,b,c,Floor[(c+b+n+1)/(a+1)]}; NestList[nxt,{3,1,3,4},90][[;;,2]] (* _Harvey P. Dale_, Nov 15 2024 *)
%Y Cf. A372982, A372983, A372985.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jul 09 2024