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 A191745 #31 Aug 28 2025 22:02:35
%S A191745 0,23,136,411,920,1735,2928,4571,6736,9495,12920,17083,22056,27911,
%T A191745 34720,42555,51488,61591,72936,85595,99640,115143,132176,150811,
%U A191745 171120,193175,217048,242811,270536,300295,332160,366203,402496,441111,482120,525595,571608
%N A191745 a(n) = 12*n^3 + 9*n^2 + 2*n.
%C A191745 Number of partitions of 12*n+2 into 4 parts.
%H A191745 Vincenzo Librandi, <a href="/A191745/b191745.txt">Table of n, a(n) for n = 0..1000</a>
%H A191745 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A191745 From _Elmo R. Oliveira_, Aug 28 2025: (Start)
%F A191745 G.f.: x*(23 + 44*x + 5*x^2)/(x-1)^4.
%F A191745 E.g.f.: x*(23 + 45*x + 12*x^2)*exp(x).
%F A191745 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%e A191745 a(1)=23: there are 23 partitions of 12*1+2=14 into 4 parts: [1,1,1,11], [1,1,2,10], [1,1,3,9], [1,1,4,8], [1,1,5,7], [1,1,6,6], [1,2,2,9], [1,2,3,8], [1,2,4,7], [1,2,5,6], [1,3,3,7], [1,3,4,6], [1,3,5,5], [1,4,4,5], [2,2,2,8], [2,2,3,7], [2,2,4,6], [2,2,5,5], [2,3,3,6], [2,3,4,5], [2,4,4,4], [3,3,3,5], [3,3,4,4].
%t A191745 Table[12n^3 + 9n^2 + 2n, {n, 0, 30}]
%t A191745 LinearRecurrence[{4,-6,4,-1},{0,23,136,411},40] (* _Harvey P. Dale_, Nov 05 2019 *)
%o A191745 (Magma) [12*n^3+9*n^2+2*n: n in [0..40]]; // _Vincenzo Librandi_, Jun 14 2011
%o A191745 (PARI) a(n)=((12*n+9)*n+2)*n /* _Charles R Greathouse IV_, Jun 14 2011 */
%K A191745 nonn,easy,changed
%O A191745 0,2
%A A191745 _Adi Dani_, Jun 14 2011