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A300445
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a(n) is the maximum value of the quartet index of a bifurcating rooted tree with n leaves.
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0
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0, 0, 0, 1, 3, 9, 19, 38, 64, 106, 162, 243, 343, 479, 645, 860, 1110, 1424, 1790, 2237, 2743, 3349, 4035, 4842, 5734, 6770, 7920, 9239, 10679, 12315, 14105, 16120, 18290, 20716, 23342, 26257, 29377, 32821, 36517, 40574, 44880, 49586, 54602, 60059, 65827, 72079, 78705, 85860, 93376, 101468
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OFFSET
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1,5
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COMMENTS
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Grows asymptotically in O(n^4).
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LINKS
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FORMULA
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a(n) = a(floor(n/2)) + a(ceiling(n/2)) + binomial(floor(n/2),2) * binomial(ceiling(n/2),2) for n>3; with a(1)=a(2)=a(3)=0.
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MATHEMATICA
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a[n_] := a[Floor[n/2]] + a[Ceiling[n/2]] + Binomial[Floor[n/2], 2]*Binomial[Ceiling[n/2], 2]; a[1] = 0; Array[a, 50] (* Robert G. Wilson v, Mar 06 2018 *)
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PROG
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(R) q=c(0, 0, 0, 1)
for (i in (4:20)){q[i]=q[floor(i/2)] + q[ceiling(i/2)] + choose(floor(i/2), 2) * choose(ceiling(i/2), 2)}
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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