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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, 47, -71, -71, 109, 109, -165, -165, 250, 250, -380, -380, 578, 578, -876, -876, 1330, 1330, -2020, -2020, 3068, 3068, -4656, -4656, 7070, 7070, -10736, -10736, 16300, 16300, -24746, -24746, 37574, 37574, -57050, -57050
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,9
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LINKS
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FORMULA
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G.f.: x^2/((1-x)*(Sum{k>=0, x^(2^k)) - x)).
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MATHEMATICA
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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}] ];
S[n_]:= Sum[(-1)^j*t[n, j], {j, 0, n}]; (* S = A104977 *)
a[n_]:= a[n]= Sum[If[EvenQ[n-k], S[(n-k)/2], 0], {k, 0, n}];
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PROG
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(Sage)
@CachedFunction
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) )
def S(n): return sum( (-1)^j*t(n, j) for j in (0..n) ) # S = A104977
def T(n, k): return S((n-k)/2) if (mod(n-k, 2)==0) else 0 # T = A104975
def a(n): return sum( T(n, k) for k in (0..n) )
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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