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%I #27 Sep 08 2022 08:45:57
%S 0,23,136,411,920,1735,2928,4571,6736,9495,12920,17083,22056,27911,
%T 34720,42555,51488,61591,72936,85595,99640,115143,132176,150811,
%U 171120,193175,217048,242811,270536,300295,332160
%N a(n) = 12*n^3 + 9*n^2 + 2*n.
%C Number of partitions of 12*n+2 into 4 parts.
%H Vincenzo Librandi, <a href="/A191745/b191745.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%e 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 Table[12n^3 + 9n^2 + 2n, {n, 0, 30}]
%t LinearRecurrence[{4,-6,4,-1},{0,23,136,411},40] (* _Harvey P. Dale_, Nov 05 2019 *)
%o (Magma) [12*n^3+9*n^2+2*n: n in [0..40]]; // _Vincenzo Librandi_, Jun 14 2011
%o (PARI) a(n)=((12*n+9)*n+2)*n /* _Charles R Greathouse IV_, Jun 14 2011 */
%K nonn,easy
%O 0,2
%A _Adi Dani_, Jun 14 2011
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