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 A050686 #14 Dec 10 2024 15:05:25 %S A050686 1,1,18,18,252,252,3168,3168,37512,37512,427608,427608,4748472, %T A050686 4748472,51736248,51736248,555626232,555626232,5900636088,5900636088, %U A050686 62105724792,62105724792,648951523128,648951523128,6740563708152 %N A050686 Number of palindromes of length n and containing the digit 1 (or any other fixed nonzero digit). %F A050686 Empirical g.f.: -x*(x-1)*(x+1)^2 / ((3*x-1)*(3*x+1)*(10*x^2-1)). - _Colin Barker_, Feb 15 2013 %F A050686 From _Sela Fried_, Dec 10 2024: (Start) %F A050686 The conjectured g.f is correct. %F A050686 a(n) = 9*10^(n/2 - 1) - 8*9^(n/2 - 1) if n is even %F A050686 a(n) = 9*10^((n - 1)/2) - 8*9^((n - 1)/2) if n is odd. (End) %e A050686 For length 3 we find 18 numbers: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 313, 414, 515, 616, 717, 818, 919. %Y A050686 Cf. A050683, A050720. %K A050686 nonn,base %O A050686 1,3 %A A050686 _Patrick De Geest_, Aug 15 1999 %E A050686 More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999