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 A016205 #22 Mar 29 2025 04:26:06 %S A016205 1,13,137,1385,13881,138873,1388857,13888825,138888761,1388888633, %T A016205 13888888377,138888887865,1388888886841,13888888884793, %U A016205 138888888880697,1388888888872505,13888888888856121,138888888888823353,1388888888888757817,13888888888888626745,138888888888888364601 %N A016205 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-10*x)). %H A016205 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-32,20). %F A016205 a(n) = (25*10^n - 9*2^n + 2)/18. - _Bruno Berselli_, Feb 09 2011 %F A016205 a(n) = 10*a(n-1) + 2^(n+1) - 1 if n > 0; a(0)=1. - _Vincenzo Librandi_, Feb 09 2011 %F A016205 From _Elmo R. Oliveira_, Mar 26 2025: (Start) %F A016205 E.g.f.: exp(x)*(25*exp(9*x) - 9*exp(x) + 2)/18. %F A016205 a(n) = 13*a(n-1) - 32*a(n-2) + 20*a(n-3). %F A016205 a(n) = A016134(n+1) - A002275(n+2). (End) %o A016205 (PARI) Vec(1/(1-13*x+32*x^2-20*x^3) + O(x^21)) \\ _Elmo R. Oliveira_, Mar 26 2025 %Y A016205 Cf. A002275, A016134. %K A016205 nonn,easy %O A016205 0,2 %A A016205 _N. J. A. Sloane_ %E A016205 More terms from _Elmo R. Oliveira_, Mar 26 2025