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A194629 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 6
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 (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) <= 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

Alois P. Heinz, Table of n, a(n) for n = 1..1000

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. Also IEEE Trans. Information Theory, Vol. 59, No. 2, 2013 pp. 1065-1075.

FORMULA

a(n) = A294775(n-1,5). - Alois P. Heinz, Nov 08 2017

MATHEMATICA

b[n_, r_, k_] := b[n, r, k] = If[n < r, 0, If[r == 0, If[n == 0, 1, 0], Sum[b[n - j, k (r - j), k], {j, 0, Min[n, r]}]]];

a[n_] := b[5n-4, 1, 6];

Array[a, 40] (* Jean-Fran├žois Alcover, Jul 21 2018, after Alois P. Heinz *)

PROG

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

CROSSREFS

Cf. A002572, A176485, A176503, A194628, A294775.

Sequence in context: A239558 A239559 A001592 * A251710 A217832 A251740

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

Invalid empirical g.f. removed by Alois P. Heinz, Nov 08 2017

STATUS

approved

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Last modified October 20 10:32 EDT 2019. Contains 328257 sequences. (Running on oeis4.)