cp's OEIS Frontend

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.

A130723 Least common multiple of 3 and n^2+n+1.

This page as a plain text file.
%I A130723 #15 Aug 18 2019 16:36:14
%S A130723 3,3,21,39,21,93,129,57,219,273,111,399,471,183,633,723,273,921,1029,
%T A130723 381,1263,1389,507,1659,1803,651,2109,2271,813,2613,2793,993,3171,
%U A130723 3369,1191,3783,3999,1407,4449,4683,1641,5169,5421,1893,5943,6213,2163,6771
%N A130723 Least common multiple of 3 and n^2+n+1.
%H A130723 Harvey P. Dale, <a href="/A130723/b130723.txt">Table of n, a(n) for n = 0..1000</a>
%H A130723 <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 A130723 From _Colin Barker_, Mar 08 2017: (Start)
%F A130723 G.f.: 3*(1 + x + 7*x^2 + 10*x^3 + 4*x^4 + 10*x^5 + 7*x^6 + x^7 + x^8) / ((1 - x)^3*(1 + x + x^2)^3).
%F A130723 a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>8.
%F A130723 (End)
%t A130723 Table[LCM[3,n^2+n+1],{n,0,60}] (* _Harvey P. Dale_, Mar 03 2017 *)
%o A130723 (PARI) a(n) = lcm(3, n^2+n+1) \\ _Michel Marcus_, Jul 11 2013
%o A130723 (PARI) Vec(3*(1 + x + 7*x^2 + 10*x^3 + 4*x^4 + 10*x^5 + 7*x^6 + x^7 + x^8) / ((1 - x)^3*(1 + x + x^2)^3) + O(x^100)) \\ _Colin Barker_, Mar 08 2017
%Y A130723 Cf. A109044.
%K A130723 easy,nonn
%O A130723 0,1
%A A130723 _W. Neville Holmes_, Jul 04 2007
%E A130723 Corrected by _Harvey P. Dale_, Mar 03 2017