A027874 Minimal degree path length of a tree with n leaves.

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

Offset: 1

Author

Don Knuth

Keywords

• nonn
• easy
• nice

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to trees

Crossrefs

Cf. A003314.

Programs

Maple

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)):
seq(a(n), n=1..60);  # Alois P. Heinz, Feb 22 2018

Mathematica

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 *)

Formula

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.

Extensions

More terms from James Sellers