1,4

Define fib(1) = 1, fib(2) = 0, and fib(n) = concat(fib(n-1), fib(n-2)). 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.

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.

Cf. A003849.

Sequence in context: A377358 A192332 A324603 * A349765 A018279 A307459

Adjacent sequences: A322517 A322518 A322519 * A322521 A322522 A322523

Jeffrey Shallit, Dec 13 2018

approved