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 A194633 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 4
 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 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-1,9). 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[9n-8, 1, 10]; Array[a, 40] (* Jean-François Alcover, Jul 21 2018, after Alois P. Heinz *) PROG (PARI) /* see A002572, set t=10 */ CROSSREFS Cf. A002572, A176485, A176503, A194628 - A194632, A294775. Sequence in context: A172319 A234591 A122265 * A243088 A113010 A292568 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 Invalid empirical g.f. removed by Alois P. Heinz, Nov 08 2017 STATUS approved

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Last modified October 20 10:18 EDT 2019. Contains 328257 sequences. (Running on oeis4.)