

A027874


Minimal degree path length of a tree with n leaves.


0



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

1,2


REFERENCES

Theorem 5.4.9L in D. E. Knuth, `The Art of Computer Programming', Volume 3.


LINKS

Table of n, a(n) for n=1..55.
Index entries for sequences related to trees


FORMULA

a(n)=3*q*n+2*(n3^q), if 2*3^(q1)<=n<=3^q; 3*q*n+4*(n3^q), if 3^q<=n<=2*3^q.


MATHEMATICA

a[n_] := For[q = 0, True, q++, If[2*3^(q1) <= n <= 3^q, Return[3*q*n + 2*(n3^q)], If[3^q <= n <= 2*3^q, Return[3*q*n + 4*(n3^q)]]]]; Array[a, 55] (* JeanFrançois Alcover, Oct 26 2015 *)


CROSSREFS

Cf. A003314.
Sequence in context: A162207 A092614 A085899 * A009850 A009853 A008030
Adjacent sequences: A027871 A027872 A027873 * A027875 A027876 A027877


KEYWORD

nonn,easy,nice


AUTHOR

Don Knuth


EXTENSIONS

More terms from James A. Sellers


STATUS

approved



