

A194632


Arises in enumerating Huffman codes, compact trees, and sums of unit fractions.


1



1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2041, 4080, 8156, 16304, 32592, 65152, 130240, 260352, 520448, 1040384, 2079746, 4157449, 8310814, 16613464, 33210608, 66388592, 132711968, 265293568, 530326528, 1060132096, 2119222786, 4236363783, 8468566033
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OFFSET

1,4


COMMENTS

a(n+1) is the number of compositions n=p(1)+p(2)+...+p(m) with p(1)=1 and p(k) <= 9*p(k+1). [Joerg Arndt, Dec 18 2012]
Row 8 of Table 1 of Elsholtz, row 1 being A002572, row 2 being A176485, row 3 being A176503, row 4 being A194628, row 5 being A194629, row 6 being A194630, and row 7 being A194631.


LINKS

Table of n, a(n) for n=1..36.
Christian Elsholtz, Clemens Heuberger, Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, arXiv:1108.5964v1 [math.CO], Aug 30, 2011.


PROG

(PARI) /* see A002572, set t=9 */


CROSSREFS

Cf. A002572, A176485, A176503, A194628, A194629, A194630, A194631.
Sequence in context: A234590 A104144 A258800 * A251759 A243087 A123464
Adjacent sequences: A194629 A194630 A194631 * A194633 A194634 A194635


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Aug 30 2011


EXTENSIONS

Added terms beyond a(20)=130240, Joerg Arndt, Dec 18 2012.


STATUS

approved



