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A027874
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Minimal degree path length of a tree with n leaves.
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1
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0, 4, 9, 16, 23, 30, 38, 46, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144, 155, 166, 177, 188, 199, 210, 221, 232, 243, 256, 269, 282, 295, 308, 321, 334, 347, 360, 373, 386, 399, 412, 425, 438, 451, 464, 477, 490, 503, 516, 529, 542, 555, 568, 581, 594, 608
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OFFSET
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1,2
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REFERENCES
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Theorem 5.4.9L in D. E. Knuth, `The Art of Computer Programming', Volume 3.
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LINKS
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FORMULA
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a(n) = 3*q*n+2*(n-3^q), if 2*3^(q-1)<=n<=3^q; 3*q*n+4*(n-3^q), if 3^q<=n<=2*3^q.
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MAPLE
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a:= n-> (q-> `if`(n>2*3^q, 3*(q+1)*n+2*(n-3^(q+1)),
3*q*n+4*(n-3^q)))(ilog[3](n)):
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MATHEMATICA
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a[n_] := For[q = 0, True, q++, If[2*3^(q-1) <= n <= 3^q, Return[3*q*n + 2*(n-3^q)], If[3^q <= n <= 2*3^q, Return[3*q*n + 4*(n-3^q)]]]]; Array[a, 55] (* Jean-François Alcover, Oct 26 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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