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 A111733 #22 Sep 08 2022 08:45:21
%S A111733 1,1,9,17,33,57,97,161,265,433,705,1145,1857,3009,4873,7889,12769,
%T A111733 20665,33441,54113,87561,141681,229249,370937,600193,971137,1571337,
%U A111733 2542481,4113825,6656313,10770145,17426465,28196617,45623089,73819713,119442809
%N A111733 a(n) = a(n-1) + a(n-2) + 7 where a(0) = a(1) = 1.
%C A111733 This is the sequence A(1,1;1,1;7)of the family of sequences [a,b:c,d:k] considered by _Gary Detlefs_, and treated as A(a,b;c,d;k) in the W. Lang link given below. - _Wolfdieter Lang_, Oct 17 2010
%H A111733 Wolfdieter Lang, <a href="/A111733/a111733.pdf">Notes on certain inhomogeneous three term recurrences.</a>
%H A111733 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1)
%F A111733 From _R. J. Mathar_, Jul 08 2009: (Start)
%F A111733 G.f.: (1-x+7*x^2)/((x-1)*(x^2+x-1)).
%F A111733 a(n) = 8*A000045(n+1) - 7 = 2*a(n-1) - a(n-3). (End)
%F A111733 a(n+1) - a(n) = A022091(n). - _R. J. Mathar_, Apr 22 2013
%e A111733 a(2) = a(0) + a(1) + 7 = 1 + 1 + 7 = 9, which is the third term in the sequence.
%t A111733 a[0] := 1; a[1] := 1; a[n_] := a[n - 1] + a[n - 2] + 7; Table[a[n], {n, 0, 30}] (* _Stefan Steinerberger_, Mar 10 2006 *)
%t A111733 LinearRecurrence[{2, 0, -1}, {1, 1, 9}, 40] (* _Vincenzo Librandi_, Sep 16 2015 *)
%o A111733 (Magma) I:=[1,1,9]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Sep 16 2015
%K A111733 nonn,easy
%O A111733 0,3
%A A111733 _Parthasarathy Nambi_, Nov 18 2005
%E A111733 More terms from _Stefan Steinerberger_, Mar 10 2006
%E A111733 More terms from Brian Lauer (bel136(AT)psu.edu), Apr 05 2006