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 A199565 #16 Mar 02 2025 21:30:55
%S A199565 2,16,142,1276,11482,103336,930022,8370196,75331762,677985856,
%T A199565 6101872702,54916854316,494251688842,4448265199576,40034386796182,
%U A199565 360309481165636,3242785330490722,29185067974416496,262665611769748462,2363990505927736156,21275914553349625402,191483230980146628616
%N A199565 a(n) = (7*9^n + 1)/4.
%H A199565 Vincenzo Librandi, <a href="/A199565/b199565.txt">Table of n, a(n) for n = 0..1000</a>
%H A199565 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A199565 a(n) = 2*A187709(n).
%F A199565 a(n) = 9*a(n-1) - 2.
%F A199565 a(n) = 10*a(n-1) - 9*a(n-2).
%F A199565 G.f.: 2*(1-2*x)/((1-x)*(1-9*x)).
%F A199565 From _Elmo R. Oliveira_, Mar 02 2025: (Start)
%F A199565 E.g.f.: exp(x)*(7*exp(8*x) + 1)/4.
%F A199565 a(n) = A199566(n)/2 = A199567(n)/4. (End)
%t A199565 LinearRecurrence[{10,-9},{2,16},30] (* _Harvey P. Dale_, Mar 14 2015 *)
%o A199565 (Magma) [(7*9^n+1)/4: n in [0..30]];
%Y A199565 Cf. A187709, A199566, A199567.
%K A199565 nonn,easy
%O A199565 0,1
%A A199565 _Vincenzo Librandi_, Nov 08 2011