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 A117917 #26 Sep 08 2022 08:45:24
%S A117917 1,4,15,52,175,582,1927,6370,21045,69514,229597,758316,2504557,
%T A117917 8272000,27320571,90233728,298021771,984299058,3250918963,10737055966,
%U A117917 35462086881,117123316630,386832036793,1277619427032,4219690317913
%N A117917 a(n) = 3*a(n-1) + a(n-2) + n.
%C A117917 a(n)/a(n-1) tends to 3.30277563... = exp(ArcSinh(3/2)) (A098316).
%H A117917 Harvey P. Dale, <a href="/A117917/b117917.txt">Table of n, a(n) for n = 0..1000</a>
%H A117917 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,1,1).
%F A117917 O.g.f.: (1 - x + x^2)/((1-x)^2*(1 - 3*x - x^2)). - _R. J. Mathar_, Mar 17 2008
%F A117917 a(n) = ( -3*n - 5 + 2*A006190(n) + 14*A006190(n+1) )/9. - _R. J. Mathar_, Oct 21 2012
%t A117917 LinearRecurrence[{5,-6,1,1},{1,4,15,52},30] (* _Harvey P. Dale_, Mar 21 2018 *)
%o A117917 (Magma) I:=[1,4,15,52]; [n le 4 select I[n] else 5*Self(n-1) -6*Self(n-2) +Self(n-3) +Self(n-4): n in [1..31]]; // _G. C. Greubel_, Oct 22 2021
%o A117917 (Sage) [(2*lucas_number1(n+2, 3, -1) + 8*lucas_number1(n+1, 3, -1) - 3*n -5)/9 for n in (0..30)] # _G. C. Greubel_, Oct 22 2021
%Y A117917 Cf. A006190.
%K A117917 nonn,easy
%O A117917 0,2
%A A117917 _Gary W. Adamson_, Apr 02 2006
%E A117917 More terms from _R. J. Mathar_, Mar 17 2008