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%I #11 Jun 09 2021 02:55:19
%S 1,1,0,0,1,1,-1,-1,2,2,-2,-2,4,4,-6,-6,9,9,-13,-13,21,21,-31,-31,47,
%T 47,-71,-71,109,109,-165,-165,250,250,-380,-380,578,578,-876,-876,
%U 1330,1330,-2020,-2020,3068,3068,-4656,-4656,7070,7070,-10736,-10736,16300,16300,-24746,-24746,37574,37574,-57050,-57050
%N Row sums of A104975.
%H G. C. Greubel, <a href="/A104976/b104976.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} A104975(n, k).
%F G.f.: x^2/((1-x)*(Sum{k>=0, x^(2^k)) - x)).
%t t[n_, k_]:= t[n, k]= If[k==n, 1, ((1+(-1)^(n-k))/2)*Sum[Binomial[k, j]*t[(n-k)/2, j], {j,(n-k)/2}] ];
%t S[n_]:= Sum[(-1)^j*t[n, j], {j,0,n}]; (* S = A104977 *)
%t a[n_]:= a[n]= Sum[If[EvenQ[n-k], S[(n-k)/2], 0], {k,0,n}];
%t Table[a[n], {n, 0, 65}] (* _G. C. Greubel_, Jun 08 2021 *)
%o (Sage)
%o @CachedFunction
%o def t(n,k): return 1 if (k==n) else ((1+(-1)^(n-k))/2)*sum( binomial(k, j)*t((n-k)/2, j) for j in (1..(n-k)//2) )
%o def S(n): return sum( (-1)^j*t(n, j) for j in (0..n) ) # S = A104977
%o def T(n,k): return S((n-k)/2) if (mod(n-k, 2)==0) else 0 # T = A104975
%o def a(n): return sum( T(n,k) for k in (0..n) )
%o [a(n) for n in (0..65)] # _G. C. Greubel_, Jun 08 2021
%Y Cf. A104975, A104977.
%K easy,sign
%O 0,9
%A _Paul Barry_, Mar 30 2005
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