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A194631 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 2
1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 255, 509, 1017, 2032, 4060, 8112, 16208, 32384, 64704, 129280, 258304, 516098, 1031177, 2060318, 4116568, 8225008, 16433776, 32835104, 65605376, 131081216, 261903618, 523290119, 1045547025, 2089029664, 4173934632 (list; graph; refs; listen; history; text; internal format)
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) <= 8*p(k+1).  [Joerg Arndt, Dec 18 2012]

Row 7 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, and row 6 being A194630.

LINKS

Table of n, a(n) for n=1..35.

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=8 */

CROSSREFS

Cf. A002572, A176485, A176503, A194628, A194629, A194630.

Sequence in context: A172317 A234589 A079262 * A251746 A251760 A243086

Adjacent sequences:  A194628 A194629 A194630 * A194632 A194633 A194634

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Aug 30 2011

EXTENSIONS

Added terms beyond a(20)=129280, Joerg Arndt, Dec 18 2012.

STATUS

approved

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Last modified June 23 13:14 EDT 2017. Contains 288665 sequences.