%I
%S 0,1,1,2,4,22,312,33143,64965951,20058315337257,
%T 15792091520191402379931,5721805662838667637519582188414354232,
%U 2170961877933428490749956608284958165048685362717276820688378
%N Word binomial coefficient for fib(n+1), fib(n), where fib(n) is the nth Fibonacci word.
%C Define fib(1) = 1, fib(2) = 0, and fib(n) = concat(fib(n1), fib(n2)). Then fib(n) is the prefix of length F(n) of the infinite Fibonacci word A003849. The word binomial coefficient for two words (x, y) is the number of occurrences of y as a (scattered) subword of x.
%e For example, if n = 5, then fib(6) = 01001010 and fib(5) = 01001, and 01001 occurs in 4 distinct ways as a subword of 01001010; so a(5) = 4.
%Y Cf. A003849.
%K nonn
%O 1,4
%A _Jeffrey Shallit_, Dec 13 2018
