|
|
A194629
|
|
Arises in enumerating Huffman codes, compact trees, and sums of unit fractions.
|
|
6
|
|
|
1, 1, 1, 2, 4, 8, 16, 32, 63, 125, 249, 496, 988, 1968, 3920, 7808, 15552, 30978, 61705, 122910, 244824, 487664, 971376, 1934880, 3854082, 7676935, 15291665, 30459424, 60672040, 120852464, 240725680, 479500802, 955116293, 1902493446, 3789571321, 7548436410
(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) <= 6*p(k+1). - Joerg Arndt, Dec 18 2012
|
|
LINKS
|
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
|
|
|
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[5n-4, 1, 6];
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Terms beyond a(20)=122910 added by Joerg Arndt, Dec 18 2012
|
|
STATUS
|
approved
|
|
|
|