OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..14
FORMULA
a(n) = A141539(2^n-1,n).
a(n) = A376091(2^n-1).
a(n) = A376033(2^n-1,2^n-1).
a(n) = 1 + Sum_{i=0..floor((2^n-2)/(n+1))} binomial(2^n-(n*i)-1,i+1). - John Tyler Rascoe, Oct 04 2024
EXAMPLE
a(0) = 1: the empty word.
a(1) = 2: 0, 1.
a(2) = 4: 000, 100, 010, 001.
a(3) = 14: 0000000, 1000000, 0100000, 0010000, 0001000, 0000100, 1000100, 0000010, 1000010, 0100010, 0000001, 1000001, 0100001, 0010001.
PROG
(Python)
from math import comb
def A376697(n): return 1 + sum(comb(2**n-(n*i)-1, i+1) for i in range(0, (2**n-2)//(n+1)+1)) # John Tyler Rascoe, Oct 04 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 02 2024
STATUS
approved