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 A193578 #17 Mar 28 2025 12:29:38 %S A193578 1,7,85,1099,14281,185647,2413405,31374259,407865361,5302249687, %T A193578 68929245925,896080197019,11649042561241,151437553296127, %U A193578 1968688192849645,25592946507045379,332708304591589921,4325207959690668967,56227703475978696565,730960145187723055339,9502481887440399719401 %N A193578 a(n) = (13^n + 1)/2. %H A193578 Vincenzo Librandi, <a href="/A193578/b193578.txt">Table of n, a(n) for n = 0..900</a> %H A193578 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-13). %F A193578 a(n) = 13*a(n-1) - 6, a(0)=1. %F A193578 From _Elmo R. Oliveira_, Mar 25 2025: (Start) %F A193578 G.f.: (1-7*x)/((1-x)*(1-13*x)). %F A193578 E.g.f.: exp(7*x)*cosh(6*x). %F A193578 a(n) = 14*a(n-1) - 13*a(n-2). %F A193578 a(n) = A141012(n+1)/2. (End) %t A193578 (13^Range[0, 20] + 1)/2 (* _Paolo Xausa_, Mar 28 2025 *) %o A193578 (Magma) [(13^n+1)/2: n in [0..20]]; %o A193578 (PARI) a(n)=(13^n+1)/2 \\ _Charles R Greathouse IV_, Dec 27 2011 %Y A193578 Cf. A141012. %K A193578 nonn,easy %O A193578 0,2 %A A193578 _Vincenzo Librandi_, Sep 17 2011