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 A169642 #28 Aug 12 2022 09:22:14
%S A169642 0,3,20,21,72,55,156,105,272,171,420,253,600,351,812,465,1056,595,
%T A169642 1332,741,1640,903,1980,1081,2352,1275,2756,1485,3192,1711,3660,1953,
%U A169642 4160,2211,4692,2485,5256,2775,5852,3081,6480,3403,7140,3741,7832,4095,8556
%N A169642 a(n) = A005408(n) * A022998(n).
%H A169642 Colin Barker, <a href="/A169642/b169642.txt">Table of n, a(n) for n = 0..1000</a>
%H A169642 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A169642 From _R. J. Mathar_, Oct 09 2010: (Start)
%F A169642 a(n)= +3*a(n-2) -3*a(n-4) +a(n-6).
%F A169642 G.f.: -x*(3+20*x+12*x^2+12*x^3+x^4)/ ( (x-1)^3*(1+x)^3 ). (End)
%F A169642 From _Colin Barker_, Dec 29 2016: (Start)
%F A169642 a(n) = 4*n^2 + 2*n for n>0 and even.
%F A169642 a(n) = 2*n^2 + n for n odd. (End)
%F A169642 Sum_{n>=1} 1/a(n) = 1 + Pi/8 - 5*log(2)/4. - _Amiram Eldar_, Aug 12 2022
%t A169642 LinearRecurrence[{0, 3, 0, -3 , 0, 1}, {0 , 3, 20, 21, 72, 55}, 47] (* _Georg Fischer_, Feb 22 2019 *)
%o A169642 (PARI) concat(0, Vec(-x*(3+20*x+12*x^2+12*x^3+x^4)/ ((x-1)^3*(1+x)^3) + O(x^50))) \\ _Colin Barker_, Dec 29 2016
%Y A169642 Cf. A005408, A022998.
%K A169642 nonn,easy
%O A169642 0,2
%A A169642 _Paul Curtz_, Apr 04 2010
%E A169642 Edited by _N. J. A. Sloane_, Apr 05 2010
%E A169642 More terms from _R. J. Mathar_, Oct 09 2010