|
|
A331699
|
|
Sum of ceiling(n/per(w)) over all binary words of length n.
|
|
4
|
|
|
2, 6, 14, 30, 60, 118, 236, 460, 914, 1810, 3608, 7158, 14310, 28504, 56978, 113778, 227484, 454534, 909050, 1817232, 3634344, 7267198, 14534120, 29064982, 58129922, 116253394, 232506236, 465000468, 929999880, 1859974762, 3719949488, 7439848936, 14879695742
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The period per(w), for w = w[1..n] a word, is the least p >= 1 such that w[i] = w[i+p] for 1 <= i <= n-p.
Asymptotically we have a(n) ~ 1.732213...*2^n.
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 3 there are two words of period 1 (000 and 111), two words of period 2 (010 and 101), and all other words are of period 3. So a(n) = 2*ceiling(3/1) + 2*ceiling(3/2) + 4*ceiling(3/3) = 14.
|
|
PROG
|
(C) See Links section.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|