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A194631 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 4
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, 8339628016 (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

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-1,7). - 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[7n-6, 1, 8];

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

PROG

(PARI) /* see A002572, set t=8 */

CROSSREFS

Cf. A002572, A176485, A176503, A194628, A194629, A194630, A294775.

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 October 20 10:45 EDT 2019. Contains 328257 sequences. (Running on oeis4.)