A129300 a(0)=1. a(n) = a(n-1) + (sum of the terms of the sequence which are <= n).
1, 2, 5, 8, 11, 19, 27, 35, 51, 67, 83, 110, 137, 164, 191, 218, 245, 272, 299, 345, 391, 437, 483, 529, 575, 621, 667, 740, 813, 886, 959, 1032, 1105, 1178, 1251, 1359, 1467, 1575, 1683, 1791, 1899, 2007, 2115, 2223, 2331, 2439, 2547, 2655, 2763, 2871, 2979
Offset: 0
Keywords
Examples
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.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Programs
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Haskell
a129300 n = a129300_list !! (n-1) a129300_list = 1 : f [1] 1 where f xs@(x:_) k = y : f (y:xs) (k+1) where y = x + sum [z | z <- xs, z <= k] -- Reinhard Zumkeller, Feb 09 2012 -
Maple
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
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Mathematica
Nest[Function[{s,n},Append[s,s[[-1]]+Total[TakeWhile[s,#<=n&]]]]@@{#,Length[#]}&,{1}, 50] (* James C. McMahon, Jan 20 2025 *)
Extensions
More terms from Emeric Deutsch, Apr 12 2007