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A025096
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a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = A000032, t = A023533.
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1
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0, 0, 1, 3, 4, 0, 0, 0, 1, 3, 4, 7, 11, 18, 29, 47, 76, 0, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2208, 3574, 5782, 9356, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39604, 64082, 103686, 167768, 271454
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OFFSET
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2,4
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LINKS
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MATHEMATICA
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A023533[n_]:= A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3]!= n, 0, 1];
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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 >;
A025096:= func< n | (&+[Lucas(k)*A023533(n+1-k): k in [1..Floor(n/2)]]) >;
(SageMath)
@CachedFunction
def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1
def A025096(n): return sum(lucas_number2(k, 1, -1)*A023533(n-k+1) for k in (1..(n//2)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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