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%I #20 May 24 2015 03:47:19
%S 1,1,2,5,12,30,73,178,434,1058,2580,6291,15341,37408,91217,222427,
%T 542374,1322546,3224947,7863835,19175478,46758223,114017050,278023561,
%U 677943348,1653123143,4031039074,9829440768,23968486545,58445679752,142516194140,347516970942
%N a(1)=1, a(n)=a(n-a(1))+a(n-a(2))+a(n-a(3))+....a(n-a(n-1)) for n>1, with convention that a(i)=0 for i<=0.
%H Reinhard Zumkeller, <a href="/A052109/b052109.txt">Table of n, a(n) for n = 1..1000</a>
%H Emmanuel Preissmann, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Preissmann/preissmann8.html">A Self-Indexed Sequence</a>, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.5.
%e a(5) = a(4)+a(4)+a(3) = 5+5+2 = 12.
%t a[1] = 1; a[n_ /; n <= 0] = 0; a[n_] := a[n] = Sum[a[n - a[k]], {k, 1, n-1}]; Table[a[n], {n, 1, 32}] (* _Jean-François Alcover_, Oct 07 2013 *)
%o (Haskell)
%o a052109 n = a052109_list !! (n-1)
%o a052109_list = 1 : f 2 [1] where
%o f n xs = z : f (n+1) (z:xs) where
%o z = sum $ map (a052109 . fromInteger) $
%o dropWhile (<= 0) $ map (n -) xs
%o -- _Reinhard Zumkeller_, Dec 02 2011
%Y Cf. A004001.
%K easy,nonn,nice
%O 1,3
%A Robert Lozyniak (11(AT)onna.com), Jan 20 2000
%E More terms from _David W. Wilson_, Feb 01 2000
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