A322520 Word binomial coefficient for fib(n+1), fib(n), where fib(n) is the n-th Fibonacci word.

0, 1, 1, 2, 4, 22, 312, 33143, 64965951, 20058315337257, 15792091520191402379931, 5721805662838667637519582188414354232, 2170961877933428490749956608284958165048685362717276820688378

Offset

1,4

Comments

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.

Links

Table of n, a(n) for n=1..13.

Example

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.

Crossrefs

Cf. A003849.

Sequence in context: A339781 A192332 A324603 * A349765 A018279 A307459

Adjacent sequences: A322517 A322518 A322519 * A322521 A322522 A322523

Keyword

nonn

Author

Jeffrey Shallit, Dec 13 2018

Status

approved