

A194629


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


4



1, 1, 1, 2, 4, 8, 16, 32, 63, 125, 249, 496, 988, 1968, 3920, 7808, 15552, 30978, 61705, 122910, 244824, 487664, 971376, 1934880, 3854082, 7676935, 15291665, 30459424, 60672040, 120852464, 240725680, 479500802, 955116293, 1902493446, 3789571321, 7548436410
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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) <= 6*p(k+1). [Joerg Arndt, Dec 18 2012]
Row 5 of Table 1 of Elsholtz, row 1 being A002572, row 2 being A176485, row 3 being A176503, and row 4 being A194628.


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.


FORMULA

Empirical g.f.: x*(x^15+x^9+x^8x^7x^2x+1) / (3*x^8x^72*x+1).  Colin Barker, May 09 2013


PROG

(PARI) /* see A002572, set t=6 */


CROSSREFS

Cf. A002572, A176485, A176503, A194628.
Sequence in context: A239558 A239559 A001592 * A217832 A140134 A049886
Adjacent sequences: A194626 A194627 A194628 * A194630 A194631 A194632


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Aug 30 2011


EXTENSIONS

Added terms beyond a(20)=122910, Joerg Arndt, Dec 18 2012.


STATUS

approved



