cp's OEIS Frontend

A194629 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions.

%I A194629 #38 Feb 15 2020 23:55:11
%S A194629 1,1,1,2,4,8,16,32,63,125,249,496,988,1968,3920,7808,15552,30978,
%T A194629 61705,122910,244824,487664,971376,1934880,3854082,7676935,15291665,
%U A194629 30459424,60672040,120852464,240725680,479500802,955116293,1902493446,3789571321,7548436410
%N A194629 Arises in enumerating Huffman codes, compact trees, and sums of unit fractions.
%C A194629 a(n+1) is the number of compositions n=p(1)+p(2)+...+p(m) with p(1)=1 and p(k) <= 6*p(k+1). - _Joerg Arndt_, Dec 18 2012
%C A194629 Row 5 of Table 1 of Elsholtz, row 1 being A002572, row 2 being A176485, row 3 being A176503, and row 4 being A194628.
%H A194629 Alois P. Heinz, <a href="/A194629/b194629.txt">Table of n, a(n) for n = 1..1000</a>
%H A194629 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.
%F A194629 a(n) = A294775(n-1,5). - _Alois P. Heinz_, Nov 08 2017
%t A194629 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 A194629 a[n_] := b[5n-4, 1, 6];
%t A194629 Array[a, 40] (* _Jean-François Alcover_, Jul 21 2018, after _Alois P. Heinz_ *)
%o A194629 (PARI) /* see A002572, set t=6 */
%Y A194629 Cf. A002572, A176485, A176503, A194628, A294775.
%K A194629 nonn
%O A194629 1,4
%A A194629 _Jonathan Vos Post_, Aug 30 2011
%E A194629 Terms beyond a(20)=122910 added by _Joerg Arndt_, Dec 18 2012
%E A194629 Invalid empirical g.f. removed by _Alois P. Heinz_, Nov 08 2017