This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376697 #22 Oct 04 2024 12:29:53
%S A376697 1,2,4,14,106,3970,2951330,601479320126,4878266198984685082072,
%T A376697 20251346657999168900614712784617499550822,
%U A376697 2947350921470608599960387502833128388134614870362931531590353774089056633192
%N A376697 Number of binary words of length 2^n-1 with at least n "0" between any two "1" digits.
%H A376697 Alois P. Heinz, <a href="/A376697/b376697.txt">Table of n, a(n) for n = 0..14</a>
%F A376697 a(n) = A141539(2^n-1,n).
%F A376697 a(n) = A376091(2^n-1).
%F A376697 a(n) = A376033(2^n-1,2^n-1).
%F A376697 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
%e A376697 a(0) = 1: the empty word.
%e A376697 a(1) = 2: 0, 1.
%e A376697 a(2) = 4: 000, 100, 010, 001.
%e A376697 a(3) = 14: 0000000, 1000000, 0100000, 0010000, 0001000, 0000100, 1000100, 0000010, 1000010, 0100010, 0000001, 1000001, 0100001, 0010001.
%o A376697 (Python)
%o A376697 from math import comb
%o A376697 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
%Y A376697 Cf. A000225, A141539, A376033, A376091.
%K A376697 nonn
%O A376697 0,2
%A A376697 _Alois P. Heinz_, Oct 02 2024