This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322052 #30 Jul 31 2021 17:46:15
%S A322052 0,1,20,299,3970,49401,590040,6850999,77919950,872348501,9645565060,
%T A322052 105583302099,1146187455930,12356291257201,132416725116080,
%U A322052 1411810959903599,14985692873919910,158445117779295501,1669465484919035100,17536209731411055499,183692631829191519890,1919390108560504143401
%N A322052 Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits.
%C A322052 See A004189 for the number that do not contain the specified string.
%H A322052 Robert Israel, <a href="/A322052/b322052.txt">Table of n, a(n) for n = 1..999</a>
%H A322052 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-101,10).
%F A322052 G.f.: x^2/((1-10*x)*(1-10*x+x^2)).
%e A322052 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.
%p A322052 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):
%p A322052 map(f, [$1..40]); # _Robert Israel_, Mar 27 2020
%Y A322052 Cf. A004189, A322053, A322054.
%Y A322052 Partial sums of A322628.
%K A322052 nonn,base
%O A322052 1,3
%A A322052 _N. J. A. Sloane_, Dec 21 2018