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 A191566 #28 Jun 30 2025 15:30:33
%S A191566 1,1,19,109,811,5581,39259,274429,1921771,13450861,94159099,659107549,
%T A191566 4613765131,32296331341,226074368539,1582520481469,11077643566891,
%U A191566 77543504575021,542804532811579,3799631728108189
%N A191566 a(n) = 7*a(n-1) + (-1)^n*6*2^(n-1).
%C A191566 A007283(n) = 3*2^n. A091629(n+1) = 6*2^n.
%C A191566 a(n) + a(n+2) = 10 * (b(n) = 2, 11, 83, 569, 4007, ...).
%C A191566 b(n+1) = 7*b(n) - (-1)^n*3*2^n.
%C A191566 Inverse binomial transform of A007613(n).
%H A191566 Vincenzo Librandi, <a href="/A191566/b191566.txt">Table of n, a(n) for n = 0..300</a>
%H A191566 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,14).
%F A191566 a(n+1) - a(n) = 18 * (0 followed by A053573(n)).
%F A191566 a(n) = (7^n + 2*(-2)^n)/3. - _Charles R Greathouse IV_, Jun 06 2011
%F A191566 G.f.: (1-4*x)/(1 - 5*x - 14*x^2). - _Bruno Berselli_, Jun 07 2011
%F A191566 a(n) = 5*a(n-1) + 14*a(n-2).
%t A191566 LinearRecurrence[{5,14},{1,1},40] (* _Harvey P. Dale_, Mar 01 2017 *)
%t A191566 CoefficientList[Series[(1 - 4*x)/(1 - 5*x - 14*x^2), {x, 0, 20}], x] (* _Stefano Spezia_, Sep 12 2018 *)
%o A191566 (PARI) a(n)=(7^n+2*(-2)^n)/3 \\ _Charles R Greathouse IV_, Jun 06 2011
%o A191566 (Magma) [(7^n+2*(-2)^n)/3: n in [0..30]]; // _Vincenzo Librandi_, Jun 07 2011
%K A191566 nonn,easy
%O A191566 0,3
%A A191566 _Paul Curtz_, Jun 06 2011