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%I #18 Oct 27 2017 02:24:05
%S 0,-1,-1,-4,-5,-2,-7,-8,-3,-10,-11,-4,-13,-14,-5,-16,-17,-6,-19,-20,
%T -7,-22,-23,-8,-25,-26,-9,-28,-29,-10,-31,-32,-11,-34,-35,-12,-37,-38,
%U -13,-40,-41,-14,-43,-44,-15,-46,-47,-16,-49,-50,-17,-52,-53,-18,-55,-56,-19,-58,-59,-20
%N The numerators of the inverse Akiyama-Tanigawa algorithm from A001045(n).
%C 0, -1, -1, -4/3, -5/3, -2, -7/3, -8/3, -3, -10/3, -11/3, -4, -13/4, -14/3, -5, = a(n)/b(n),
%C 1, 0, 1, 4/3, 5/3, 2, 7/3, 8/3, 3,
%C 1, -2, -1, -4/3, -5/3, -2, -7/3, -8/3, -3,
%C 3, -2, 1, 4/3, 5/3, 2, 7/3, 8/3, 3,
%C 5, -6, -1, -4/3, -5/3, -2, -7/3, -8/3, -3,
%C 11, -10, 1, 4/3, 5/3, 2, 7/3, 8/3, 3,
%C 21, -22, -1, -4/3, -5/3, -2, -7/3, -8/3, -3,
%C Vertical: A001045(n), -A078008(n), (-1)^(n+1)*A000012(n), (-1)^(n+1)*A010709(n)/A010701(n), (-1)^(n+1)*A010716(n+1)/A010701(n), A007395(n), .. .
%C a(n)=0, 1 before (-A145064(n+1)=-A051176(n+3).
%C b(n)=1, 1 before A169609(n). b(n)=1, 1, 1 before A144437(n+1).
%C a(n+5)-a(n+2)=b(n+5) (=-1,-3,-3,=-A169609(n)).
%H G. C. Greubel, <a href="/A194880/b194880.txt">Table of n, a(n) for n = 0..5000</a>
%H D. Merlini, R. Sprugnoli, M. C. Verri, <a href="http://www.emis.de/journals/INTEGERS/papers/f5/f5.Abstract.html">The Akiyama-Tanigawa Transformation</a>, Integers, 5 (1) (2005) #A05.
%F a(3*n)=-3*n-1 except a(0)=0; a(3*n+1=-3*n-2 except a(1)=-1; a(3*n+2)=-n-1.
%t a[0]=0; a[1]=-1; a[n_] := (-n-1)/Max[1, 2*Mod[n, 3]-1]; Table[a[n], {n, 0, 59}] (* _Jean-François Alcover_, Sep 18 2012 *)
%K sign,tabl,frac
%O 0,4
%A _Paul Curtz_, Sep 07 2011
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