The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A194630 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions. 5
 1, 1, 1, 2, 4, 8, 16, 32, 64, 127, 253, 505, 1008, 2012, 4016, 8016, 16000, 31936, 63744, 127234, 253961, 506910, 1011800, 2019568, 4031088, 8046112, 16060160, 32056322, 63984903, 127714833, 254920736, 508825640, 1015623664, 2027200176, 4046322176, 8076520194 (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) <= 7*p(k+1). - Joerg Arndt, Dec 18 2012 Row 6 of Table 1 of Elsholtz, row 1 being A002572, row 2 being A176485, row 3 being A176503, row 4 being A194628, and row 5 being A194629. 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-1,6). - 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[6n-5, 1, 7]; Array[a, 40] (* Jean-François Alcover, Jul 21 2018, after Alois P. Heinz *) PROG (PARI) /* see A002572, set t=7 */ CROSSREFS Cf. A002572, A176485, A176503, A194628, A194629, A294775. Sequence in context: A239560 A066178 A122189 * A251672 A251747 A251761 Adjacent sequences: A194627 A194628 A194629 * A194631 A194632 A194633 KEYWORD nonn AUTHOR Jonathan Vos Post, Aug 30 2011 EXTENSIONS Terms beyond a(20)=127234 added by Joerg Arndt, Dec 18 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 4 04:05 EST 2023. Contains 360045 sequences. (Running on oeis4.)