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A129299 a(1)=1, a(n) = a(n-1) + (sum of the earlier terms of the sequence which are <= n).

%I A129299 #20 Jan 20 2025 16:26:27
%S A129299 1,2,5,8,16,24,32,48,64,80,96,112,128,144,160,192,224,256,288,320,352,
%T A129299 384,416,472,528,584,640,696,752,808,864,952,1040,1128,1216,1304,1392,
%U A129299 1480,1568,1656,1744,1832,1920,2008,2096,2184,2272,2408,2544,2680,2816
%N A129299 a(1)=1, a(n) = a(n-1) + (sum of the earlier terms of the sequence which are <= n).
%H A129299 Reinhard Zumkeller, <a href="/A129299/b129299.txt">Table of n, a(n) for n = 1..10000</a>
%e A129299 The terms that are <= 9 are a(1) through a(4). So a(9) = a(8) + a(1) + a(2) + a(3) + a(4) = 48 + 1 + 2 + 5 + 8 = 64.
%p A129299 a[1]:=1: for n from 2 to 60 do b:=a[n-1]: for j from 1 to n-1 do if a[j]<=n then b:=b+a[j] else b:=b: fi: od: a[n]:=b: od: seq(a[n],n=1..60); # _Emeric Deutsch_, Apr 10 2007
%t A129299 s={1};Do[AppendTo[s,s[[-1]]+Total[Select[s,#<=n&]]],{n,2,51}];s (* _James C. McMahon_, Jan 20 2025 *)
%o A129299 (Haskell)
%o A129299 a129299 n = a129299_list !! (n-1)
%o A129299 a129299_list = 1 : f [1] 2 where
%o A129299    f xs@(x:_) k = y : f (y:xs) (k+1) where
%o A129299      y = x + sum [z | z <- xs, z <= k]
%o A129299 -- _Reinhard Zumkeller_, Feb 09 2012
%Y A129299 Cf. A129300, A126022, A095114.
%K A129299 nonn
%O A129299 1,2
%A A129299 _Leroy Quet_, Apr 08 2007
%E A129299 More terms from _Emeric Deutsch_, Apr 10 2007