A322052 Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits.

0, 1, 20, 299, 3970, 49401, 590040, 6850999, 77919950, 872348501, 9645565060, 105583302099, 1146187455930, 12356291257201, 132416725116080, 1411810959903599, 14985692873919910, 158445117779295501, 1669465484919035100, 17536209731411055499, 183692631829191519890, 1919390108560504143401

Offset: 1

Author

N. J. A. Sloane, Dec 21 2018

Keywords

• nonn
• base

Comments

See A004189 for the number that do not contain the specified string.

Examples

			Suppose the desired string is 03. At length 2 that is the only possibility. At length 3 there are 20 strings that contain it: 03d and d03, where d is any digit.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..999
• Index entries for linear recurrences with constant coefficients, signature (20,-101,10).

Crossrefs

Cf. A004189, A322053, A322054.

Partial sums of A322628.

Programs

Maple

f:= gfun:-rectoproc({10*a(n) - 101*a(n + 1) + 20*a(n + 2) - a(n + 3), a(0) = 0, a(1) = 0, a(2) = 1},a(n),remember):
map(f, [$1..40]); # Robert Israel, Mar 27 2020

Formula

G.f.: x^2/((1-10*x)*(1-10*x+x^2)).