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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,138
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..5000
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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}];
Table[A025125[n], {n, 130}] (* G. C. Greubel, Sep 14 2022 *)
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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 >;
A025125:= func< n | (&+[A023533(k)*A023533(n+2-k): k in [1..Floor((n+1)/2)]]) >;
[A025125(n): n in [1..130]]; // G. C. Greubel, Sep 14 2022
(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))
[A025125(n) for n in (1..130)] # G. C. Greubel, Sep 14 2022
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CROSSREFS
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Cf. A023533.
Sequence in context: A353489 A288106 A286939 * A147873 A103589 A305388
Adjacent sequences: A025122 A025123 A025124 * A025126 A025127 A025128
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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