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A068915 a(n) = n if n<2; a(n) = |a(n/2)-a(n/2-1)| if n is even, and a(n) = a((n-1)/2) + a((n-1)/2+1) if n is odd. 1

%I #13 Nov 17 2020 09:46:00

%S 0,1,1,2,0,3,1,2,2,3,3,4,2,3,1,4,0,5,1,6,0,7,1,6,2,5,1,4,2,5,3,4,4,5,

%T 5,6,4,7,5,6,6,7,7,8,6,7,5,8,4,7,3,6,4,5,3,6,2,7,3,8,2,7,1,8,0,9,1,10,

%U 0,11,1,10,2,11,3,12,2,11,1,12,0,13,1,14,0,15,1,14,2,13,1,12,2,13,3,12,4,11,3,10,4,9,3,10,2,9,1,8,2,9,3,8,4,9,5,10,4,11,5,10

%N a(n) = n if n<2; a(n) = |a(n/2)-a(n/2-1)| if n is even, and a(n) = a((n-1)/2) + a((n-1)/2+1) if n is odd.

%H Alois P. Heinz, <a href="/A068915/b068915.txt">Table of n, a(n) for n = 0..10000</a>

%e a(2) = |1-0| = 1, a(3) = 1+1 = 2, a(4) = |1-1| = 0, a(5) = 1+2 = 3.

%p a:= proc(n) option remember;

%p if n<2 then n

%p elif irem (n, 2)=0 then abs(a(n/2)-a(n/2-1))

%p else a((n-1)/2)+a((n-1)/2+1)

%p fi

%p end:

%p seq (a(n), n=0..119);

%t a[n_] := a[n] = If[n<2, n, If[EvenQ[n], Abs[a[n/2] - a[n/2-1]], a[(n-1)/2] + a[(n-1)/2 + 1]]];

%t a /@ Range[0, 119] (* _Jean-Fran├žois Alcover_, Nov 17 2020 *)

%K easy,nonn

%O 0,4

%A Aaron K. Johnson (akj(AT)21stcentury.net), Mar 06 2002

%E Edited by _Alois P. Heinz_, Feb 04 2011

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