%I #26 Sep 08 2022 08:45:57
%S 1,1,19,109,811,5581,39259,274429,1921771,13450861,94159099,659107549,
%T 4613765131,32296331341,226074368539,1582520481469,11077643566891,
%U 77543504575021,542804532811579,3799631728108189
%N a(n) = 7*a(n-1) + (-1)^n*6*2^(n-1).
%C A007283(n) = 3*2^n. A091629(n+1) = 6*2^n.
%C a(n) + a(n+2) = 10 * (b(n) = 2, 11, 83, 569, 4007, ...).
%C b(n+1) = 7*b(n) - (-1)^n*3*2^n.
%C Inverse binomial transform of A007613(n).
%H Vincenzo Librandi, <a href="/A191566/b191566.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,14).
%F a(n+1) - a(n) = 18 * (0 followed by A053573(n)).
%F a(n) = (7^n + 2*(-2)^n)/3. - _Charles R Greathouse IV_, Jun 06 2011
%F G.f.: (1-4*x)/(1 - 5*x - 14*x^2). - _Bruno Berselli_, Jun 07 2011
%F a(n) = 5*a(n-1) + 14*a(n-2).
%t LinearRecurrence[{5,14},{1,1},40] (* _Harvey P. Dale_, Mar 01 2017 *)
%t CoefficientList[Series[(1 - 4*x)/(1 - 5*x - 14*x^2), {x, 0, 20}], x] (* _Stefano Spezia_, Sep 12 2018 *)
%o (PARI) a(n)=(7^n+2*(-2)^n)/3 \\ _Charles R Greathouse IV_, Jun 06, 2011
%o (Magma) [(7^n+2*(-2)^n)/3: n in [0..30]]; // _Vincenzo Librandi_, Jun 07 2011
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Jun 06 2011