A052109 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.

1, 1, 2, 5, 12, 30, 73, 178, 434, 1058, 2580, 6291, 15341, 37408, 91217, 222427, 542374, 1322546, 3224947, 7863835, 19175478, 46758223, 114017050, 278023561, 677943348, 1653123143, 4031039074, 9829440768, 23968486545, 58445679752, 142516194140, 347516970942

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Emmanuel Preissmann, A Self-Indexed Sequence, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.5.

Example

a(5) = a(4)+a(4)+a(3) = 5+5+2 = 12.

Mathematica

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 *)

Prog

(Haskell)
a052109 n = a052109_list !! (n-1)
a052109_list = 1 : f 2 [1] where
   f n xs = z : f (n+1) (z:xs) where
     z = sum $ map (a052109 . fromInteger) $
                   dropWhile (<= 0) $ map (n -) xs
-- Reinhard Zumkeller, Dec 02 2011

Crossrefs

Cf. A004001.

Sequence in context: A291253 A348619 A101911 * A157748 A046170 A369145

Adjacent sequences: A052106 A052107 A052108 * A052110 A052111 A052112

Keyword

easy,nonn,nice

Author

Robert Lozyniak (11(AT)onna.com), Jan 20 2000

Extensions

More terms from David W. Wilson, Feb 01 2000

Status

approved