cp's OEIS Frontend

A129300 a(0)=1. a(n) = a(n-1) + (sum of the terms of the sequence which are <= n).

%I A129300 #20 Jan 21 2025 03:27:05
%S A129300 1,2,5,8,11,19,27,35,51,67,83,110,137,164,191,218,245,272,299,345,391,
%T A129300 437,483,529,575,621,667,740,813,886,959,1032,1105,1178,1251,1359,
%U A129300 1467,1575,1683,1791,1899,2007,2115,2223,2331,2439,2547,2655,2763,2871,2979
%N A129300 a(0)=1. a(n) = a(n-1) + (sum of the terms of the sequence which are <= n).
%H A129300 Reinhard Zumkeller, <a href="/A129300/b129300.txt">Table of n, a(n) for n = 0..10000</a>
%e A129300 The terms that are <= 9 are a(0) through a(3). So a(9) = a(8) + a(0) + a(1) + a(2) + a(3) = 51 + 1 + 2 + 5 + 8 = 67.
%p A129300 a[0]:=1: for n from 1 to 60 do b:=0: for j from 0 to n-1 do if a[j]<=n then b:=b+a[j] else fi od: a[n]:=a[n-1]+b: od: seq(a[n],n=0..60); # _Emeric Deutsch_, Apr 12 2007
%t A129300 Nest[Function[{s,n},Append[s,s[[-1]]+Total[TakeWhile[s,#<=n&]]]]@@{#,Length[#]}&,{1}, 50] (* _James C. McMahon_, Jan 20 2025 *)
%o A129300 (Haskell)
%o A129300 a129300 n = a129300_list !! (n-1)
%o A129300 a129300_list = 1 : f [1] 1 where
%o A129300    f xs@(x:_) k = y : f (y:xs) (k+1) where
%o A129300      y = x + sum [z | z <- xs, z <= k]
%o A129300 -- _Reinhard Zumkeller_, Feb 09 2012
%Y A129300 Cf. A129299, A126022, A095114.
%K A129300 nonn
%O A129300 0,2
%A A129300 _Leroy Quet_, Apr 08 2007
%E A129300 More terms from _Emeric Deutsch_, Apr 12 2007