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 A194632 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 3
 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2041, 4080, 8156, 16304, 32592, 65152, 130240, 260352, 520448, 1040384, 2079746, 4157449, 8310814, 16613464, 33210608, 66388592, 132711968, 265293568, 530326528, 1060132096, 2119222786, 4236363783, 8468566033 (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) <= 9*p(k+1). - Joerg Arndt, Dec 18 2012 Row 8 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, and row 7 being A194631. 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:1108.5964 [math.CO], Aug 30, 2011. Also IEEE Trans. Information Theory, Vol. 59, No. 2, 2013 pp. 1065-1075. FORMULA a(n) = A294775(n-1,8). - 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[8n-7, 1, 9]; Array[a, 40] (* Jean-François Alcover, Jul 21 2018, after Alois P. Heinz *) PROG (PARI) /* see A002572, set t=9 */ CROSSREFS Cf. A002572, A176485, A176503, A194628, A194629, A194630, A194631, A294775. Sequence in context: A234590 A104144 A258800 * A282584 A251759 A243087 Adjacent sequences:  A194629 A194630 A194631 * A194633 A194634 A194635 KEYWORD nonn AUTHOR Jonathan Vos Post, Aug 30 2011 EXTENSIONS Terms beyond a(20)=130240 added by Joerg Arndt, Dec 18 2012 STATUS approved

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Last modified July 4 12:10 EDT 2022. Contains 355075 sequences. (Running on oeis4.)