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 A061171 #24 Sep 08 2022 08:45:03
%S A061171 3,19,79,283,940,2982,9171,27581,81557,237995,687158,1966764,5588259,
%T A061171 15780103,44323195,123920827,345062176,957403026,2647935987,
%U A061171 7302634865,20087869313,55128445259,150971982314
%N A061171 One half of second column of Lucas bisection triangle (odd part).
%C A061171 Numerator of g.f. is on half of row polynomial Sum_{m=0..2} A061187(1,m) * x^m.
%H A061171 G. C. Greubel, <a href="/A061171/b061171.txt">Table of n, a(n) for n = 0..1000</a>
%H A061171 É. Czabarka, R. Flórez, L. Junes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Florez/florez12.html">A Discrete Convolution on the Generalized Hosoya Triangle</a>, Journal of Integer Sequences, 18 (2015), #15.1.6.
%H A061171 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
%F A061171 2*a(n) = A060924(n+1, 1).
%F A061171 G.f.: (1+x)*(3-2*x)/(1-3*x+x^2)^2.
%F A061171 a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4), with a(0)=3, a(1)=19, a(2)=79, a(3)=283. - _Harvey P. Dale_, Oct 11 2012
%F A061171 a(n) = Fibonacci(2*n+4) + n*Lucas(2*n+3). - _Lechoslaw Ratajczak_, May 06 2020
%t A061171 CoefficientList[Series[(1+x)(3-2x)/(1-3x+x^2)^2,{x,0,30}],x] (* or *) LinearRecurrence[{6,-11,6,-1},{3,19,79,283},30] (* _Harvey P. Dale_, Oct 11 2012 *)
%o A061171 (PARI) my(x='x+O('x^30)); Vec((1+x)*(3-2*x)/(1-3*x+x^2)^2) \\ _G. C. Greubel_, Dec 21 2017
%o A061171 (Magma) I:=[3,19,79,283]; [n le 4 select I[n] else 6*Self(n-1) - 11*Self(n-2) + 6*Self(n-3) - Self(n-4): n in [1..30]]; // _G. C. Greubel_, Dec 21 2017
%Y A061171 Cf. A000032, A000045, A001906, A002878, A005248.
%K A061171 nonn,easy
%O A061171 0,1
%A A061171 _Wolfdieter Lang_, Apr 20 2001