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A194633 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 2
1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4089, 8176, 16348, 32688, 65360, 130688, 261312, 522496, 1044736, 2088960, 4176896, 8351746, 16699401, 33390622, 66764888, 133497072, 266928752, 533726752, 1067192064, 2133861376, 4266677504, 8531265024 (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) <= 10*p(k+1).  [Joerg Arndt, Dec 18 2012]

Row 9 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, row 7 being A194631, and row 8 being A194632.

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^2 +x -1)*(x^13 -x^12 -x^2 -x +1) / ((x -1)*(3*x^13 +x^12 +x^11 +x^10 +x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 -x^2 -2*x +1)). - Colin Barker, May 09 2013

PROG

(PARI) /* see A002572, set t=10 */

CROSSREFS

Cf. A002572, A176485, A176503,  A194628 - A194632.

Sequence in context: A172319 A234591 A122265 * A243088 A113010 A056767

Adjacent sequences:  A194630 A194631 A194632 * A194634 A194635 A194636

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Aug 30 2011

EXTENSIONS

Added terms beyond a(20)=130688, Joerg Arndt, Dec 18 2012.

STATUS

approved

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Last modified August 23 06:19 EDT 2017. Contains 290958 sequences.