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 A144314 #39 May 11 2025 01:15:19
%S A144314 0,21,78,171,300,465,666,903,1176,1485,1830,2211,2628,3081,3570,4095,
%T A144314 4656,5253,5886,6555,7260,8001,8778,9591,10440,11325,12246,13203,
%U A144314 14196,15225,16290,17391,18528,19701,20910,22155,23436,24753,26106,27495
%N A144314 a(n) = 3*n*(6*n + 1).
%H A144314 Harvey P. Dale, <a href="/A144314/b144314.txt">Table of n, a(n) for n = 0..1000</a>
%H A144314 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A144314 a(n) = A000217(6*n) = A014105(3*n) = A081266(2*n).
%F A144314 G.f.: 3*x*(7+5*x)/(1-x)^3. - _Vincenzo Librandi_, Dec 18 2014
%F A144314 From _Wesley Ivan Hurt_, Dec 16 2015: (Start)
%F A144314 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
%F A144314 a(n) = 3 * A049453(n). (End)
%F A144314 E.g.f.: 3*exp(x)*x*(7 + 6*x). - _Stefano Spezia_, Jun 29 2021
%F A144314 From _Amiram Eldar_, May 11 2025: (Start)
%F A144314 Sum_{n>=1} 1/a(n) = 2 - Pi/(2*sqrt(3)) - 2*log(2)/3 - log(3)/2.
%F A144314 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/3 + log(2)/3 + log(2+sqrt(3))/sqrt(3) - 2. (End)
%p A144314 A144314:=n->3*n*(6*n+1): seq(A144314(n), n=0..70); # _Wesley Ivan Hurt_, Dec 16 2015
%t A144314 Table[3n(6n+1),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,21,78},40] (* _Harvey P. Dale_, Dec 17 2014 *)
%t A144314 CoefficientList[Series[x (21 + 15 x) / (1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 18 2014 *)
%o A144314 (Magma) [18*n^2+3*n: n in [0..50]]; // _Vincenzo Librandi_, Dec 18 2014
%o A144314 (PARI) a(n)=3*n*(6*n+1) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A144314 Cf. A000217, A014105, A033585, A049453, A081266, A144312.
%K A144314 nonn,easy
%O A144314 0,2
%A A144314 _Reinhard Zumkeller_, Sep 17 2008