OFFSET
1,2
COMMENTS
All entries are odd. There are A001190(n) occurrences of 2n-1 in this sequence.
a(n) is the number of vertices in the rooted binary tree (every vertex 0 or 2 children) with Colijn-Plazzotta tree number n. - Kevin Ryde, Jul 25 2022
LINKS
Kevin Ryde, Table of n, a(n) for n = 1..10000
C. Colijn and G. Plazzotta, A Metric on Phylogenetic Tree Shapes, Systematic Biology, 67 (1) (2018), 113-126.
Kevin Ryde, PARI/GP Code
Wikipedia, Colexicographic order
FORMULA
a(n) = 2*A064064(n-1) - 1. - Kevin Ryde, Jul 25 2022
EXAMPLE
a(2) = a(1)+a(1)+1 = 3,
a(3) = a(1)+a(2)+1 = 5,
a(4) = a(2)+a(2)+1 = 7,
a(5) = a(1)+a(3)+1 = 7, ...
PROG
(PARI) See links.
(Python)
from itertools import count, islice
def bgen(): yield from ((i, j) for j in count(1) for i in range(1, j+1))
def agen():
a, g = [None, 1], bgen()
for n in count(2):
yield a[-1];
i, j = next(g)
a.append(a[i] + a[j] + 1)
print(list(islice(agen(), 72))) # Michael S. Branicky, Jul 25 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Claude Lenormand (claude.lenormand(AT)free.fr), Sep 14 2001
STATUS
approved