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 A130770 #21 Sep 08 2022 08:45:30
%S A130770 1,1,7,13,7,31,43,19,73,91,37,133,157,61,211,241,91,307,343,127,421,
%T A130770 463,169,553,601,217,703,757,271,871,931,331,1057,1123,397,1261,1333,
%U A130770 469,1483,1561,547,1723,1807,631,1981,2071,721,2257,2353,817,2551,2653,919
%N A130770 One third of the least common multiple of 3 and n^2+n+1.
%C A130770 This is a subset of A051176 and is also one third of A130723.
%H A130770 G. C. Greubel, <a href="/A130770/b130770.txt">Table of n, a(n) for n = 0..5000</a>
%H A130770 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 3, 0, 0, -3, 0, 0, 1).
%F A130770 Conjecture: a(n) = A046163(n), n>0. - _R. J. Mathar_, Jun 13 2008
%F A130770 a(n) = 3*a(n-3)-3*a(n-6)+a(n-9), with a(0)=1, a(1)=1, a(2)=7, a(3)=13, a(4)=7, a(5)=31, a(6)=43, a(7)=19, a(8)=73. - _Harvey P. Dale_, Apr 10 2014
%e A130770 a(4)=7 because 4^2+4+1 =21, the LCM of 3 and 21 is 21 and 21/3=7.
%p A130770 seq(denom((n-1)^2/(n^2+n+1)), n=0..52) ; # _Zerinvary Lajos_, Jun 04 2008
%t A130770 Table[LCM[3,n^2+n+1]/3,{n,0,60}] (* or *) LinearRecurrence[ {0,0,3,0,0,-3,0,0,1},{1,1,7,13,7,31,43,19,73},60] (* _Harvey P. Dale_, Apr 10 2014 *)
%o A130770 (PARI) for(n=0,50, print1(lcm(3, n^2 + n +1)/3, ", ")) \\ _G. C. Greubel_, Oct 26 2017
%o A130770 (Magma) [Lcm(3,n^2+n+1)/3: n in [0..50]]; // _G. C. Greubel_, Oct 26 2017
%Y A130770 Cf. A051176, A130723.
%K A130770 easy,nonn
%O A130770 0,3
%A A130770 _W. Neville Holmes_, Jul 14 2007