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a(n+1) = a(n)+a(a(a(..(n-1)..))), depth [ n/2 ].
(Formerly M0455)
3

%I M0455 #17 Aug 28 2016 18:23:35

%S 1,0,1,1,1,1,2,3,4,5,5,5,6,7,8,9,9,9,10,11,11,11,12,13,14,15,15,15,16,

%T 17,17,17,18,19,19,19,20,21,21,21,22,23,24,25,25,25,26,27,27,27,28,29,

%U 29,29,30,31,31,31,32,33,33,33,34,35,35,35,36,37,37,37,38,39,39,39,40

%N a(n+1) = a(n)+a(a(a(..(n-1)..))), depth [ n/2 ].

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A007599/b007599.txt">Table of n, a(n) for n = 0..1000</a>

%t a[n_Integer] := a[n] = (a[n - 1] + Nest[a, n - 2, Floor[n/2] ] ); a[0] = 1; a[1] = 0; Table[ a[n], {n, 0, 75} ]

%o (Haskell)

%o a007599 n = a007599_list !! n

%o a007599_list = 1 : f 1 1 where

%o f x m = y : f y (m + 1) where

%o y = x + (iterate a007599 (m-2)) !! (m `div` 2)

%o -- _Reinhard Zumkeller_, Jan 05 2012

%K nonn,nice,easy

%O 0,7

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_