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 A322053 #12 Dec 21 2018 22:06:53 %S A322053 0,1,19,280,3691,45739,544870,6315481,71743159,802527760,8868438271, %T A322053 97038694279,1053164192950,11351825985061,121644911602099, %U A322053 1296970638284440,13767539948978851,145580595285369619,1534133217109136230,16117424311550552641 %N A322053 Number of decimal strings of length n that contain a specific string xx (where x is a single digit). %C A322053 See A322054 for the number that do not contain the specified string. %F A322053 G.f. = x^2/((1-10*x)*(1-9*x-9*x^2)). %e A322053 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. %Y A322053 Cf. A322052, A004189, A322054. %Y A322053 Suggested by A322628. %K A322053 nonn,base %O A322053 1,3 %A A322053 _N. J. A. Sloane_, Dec 21 2018