A322053 Number of decimal strings of length n that contain a specific string xx (where x is a single digit).

0, 1, 19, 280, 3691, 45739, 544870, 6315481, 71743159, 802527760, 8868438271, 97038694279, 1053164192950, 11351825985061, 121644911602099, 1296970638284440, 13767539948978851, 145580595285369619, 1534133217109136230, 16117424311550552641

Offset: 1

Author

N. J. A. Sloane, Dec 21 2018

Keywords

• nonn
• base

Comments

See A322054 for the number that do not contain the specified string.

Examples

			Suppose the desired string is 00. At length 2 that is the only possibility. At length 3 there are 19 strings that contain it: 000, 00d, and d00, where d is any nonzero digit.
		

Crossrefs

Cf. A322052, A004189, A322054.

Suggested by A322628.

Formula

G.f. = x^2/((1-10*x)*(1-9*x-9*x^2)).