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A025125
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a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n-k+1), where k = floor(n/2), s = A023533.
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1
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0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
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refs;
listen;
history;
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internal format)
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OFFSET
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1,138
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LINKS
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MATHEMATICA
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b[j_]:= b[j]= Sum[KroneckerDelta[j, Binomial[m+2, 3]], {m, 0, 15}];
A025125[n_]:= A025125[n]= Sum[b[n -j+1]*b[j+1], {j, Floor[(n+2)/2], n}];
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PROG
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(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
(SageMath)
@CachedFunction
def b(j): return sum(bool(j==binomial(m+2, 3)) for m in (0..15))
@CachedFunction
def A025125(n): return sum(b(n-j+1)*b(j+1) for j in (((n+2)//2)..n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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