A176463 Irregular triangle read by rows: T(n,k) = number of Huffman-equivalence classes of ternary trees with 3n+1 leaves and 4k leaves on the bottom level (n>=1, k>=1).

1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 8, 4, 2, 1, 15, 8, 4, 2, 29, 15, 8, 4, 1, 57, 29, 15, 8, 2, 1, 112, 57, 29, 15, 4, 2, 1, 220, 112, 57, 29, 7, 4, 2

Offset

1,5

Links

Table of n, a(n) for n=1..44.

Christian Elsholtz, Clemens Heuberger and Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Trans. Information Theory, Vol. 59, No. 2, 2013 pp. 1065-1075; also arXiv:1108.5964 [math.CO], 2011.

Jordan Paschke, Jeffrey Burkert and Rebecca Fehribach, Computing and estimating the number of n-ary Huffman sequences of a specified length, Discrete Math., 311 (2011), 1-7.

Example

Triangle begins:
1
1
1 1
2 1 1
4 2 1 1
8 4 2 1
15 8 4 2
29 15 8 4 1
57 29 15 8 2 1
112 57 29 15 4 2 1
220 112 57 29 7 4 2

Crossrefs

Cf. A176431, A176452, A194628 - A194633. Leading column gives A176503.

Sequence in context: A152568 A155038 A057728 * A098050 A278984 A111579

Adjacent sequences: A176460 A176461 A176462 * A176464 A176465 A176466

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Dec 07 2010

Status

approved