OFFSET
0,2
COMMENTS
The sequence starts like the powers of 2 and then duplicate descendants start to appear at n=8: [4,5,4,4,5,4] is both [1,1,1,3,4,3]+[3,4,3,1,1,1] and [1,3,2,2,2,3]+[3,2,2,2,3,1] but is only counted once; in imaged terms, a child can have several parents.
EXAMPLE
n=
0 1 2 3 ...
+---[1,1,1,1]
|
+---[1,1,1]
| |
| +----[2,2,2]
|
+---[1,1]
| |
| | +----[2,2,1]
| | |
| +----[2,2]
| |
| +-----[4,4]
|
[1] ...
|
| +----[2,1,1]
| |
| +----[2,1]
| | |
| | +-----[3,3]
| |
+----[2]
|
| +-----[4,1]
| |
+-----[4]
|
+------[8]
a(n)=
1 2 4 8 ...
MAPLE
b:= proc(n) option remember; `if`(n=0, {[1]}, map(l->
[[l[], 1], l+ListTools[Reverse](l)][], b(n-1)))
end:
a:= n-> nops(b(n)):
seq(a(n), n=0..20); # Alois P. Heinz, Mar 04 2026
PROG
(Python)
from itertools import islice
def agen(): # generator of terms
reach = {(1, )}
while True:
yield len(reach)
out = set()
for L in reach:
out.add(L+(1, ))
out.add(tuple(t+r for t, r in zip(L, L[::-1])))
reach = out
print(list(islice(agen(), 22))) # Michael S. Branicky, Mar 18 2026
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Luc Rousseau, Mar 04 2026
EXTENSIONS
a(23) from Alois P. Heinz, Mar 04 2026
a(24)-a(26) from Michael S. Branicky, Mar 18 2026
STATUS
approved