cp's OEIS Frontend

A194632 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions.

%I A194632 #26 May 31 2021 17:09:36
%S A194632 1,1,1,2,4,8,16,32,64,128,256,511,1021,2041,4080,8156,16304,32592,
%T A194632 65152,130240,260352,520448,1040384,2079746,4157449,8310814,16613464,
%U A194632 33210608,66388592,132711968,265293568,530326528,1060132096,2119222786,4236363783,8468566033
%N A194632 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions.
%C A194632 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
%C A194632 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.
%H A194632 Alois P. Heinz, <a href="/A194632/b194632.txt">Table of n, a(n) for n = 1..1000</a>
%H A194632 Christian Elsholtz, Clemens Heuberger, Helmut Prodinger, <a href="https://arxiv.org/abs/1108.5964">The number of Huffman codes, compact trees, and sums of unit fractions</a>, arXiv:1108.5964 [math.CO], Aug 30, 2011. Also IEEE Trans. Information Theory, Vol. 59, No. 2, 2013 pp. 1065-1075.
%F A194632 a(n) = A294775(n-1,8). - _Alois P. Heinz_, Nov 08 2017
%t A194632 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]}]]];
%t A194632 a[n_] := b[8n-7, 1, 9];
%t A194632 Array[a, 40] (* _Jean-François Alcover_, Jul 21 2018, after _Alois P. Heinz_ *)
%o A194632 (PARI) /* see A002572, set t=9 */
%Y A194632 Cf. A002572, A176485, A176503, A194628, A194629, A194630, A194631, A294775.
%K A194632 nonn
%O A194632 1,4
%A A194632 _Jonathan Vos Post_, Aug 30 2011
%E A194632 Terms beyond a(20)=130240 added by _Joerg Arndt_, Dec 18 2012