A176463 - OEIS

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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

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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

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