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 A016946 #42 Jul 08 2025 06:00:36
%S A016946 9,81,225,441,729,1089,1521,2025,2601,3249,3969,4761,5625,6561,7569,
%T A016946 8649,9801,11025,12321,13689,15129,16641,18225,19881,21609,23409,
%U A016946 25281,27225,29241,31329,33489,35721,38025,40401,42849,45369,47961,50625,53361,56169
%N A016946 a(n) = (6*n+3)^2.
%H A016946 Vincenzo Librandi, <a href="/A016946/b016946.txt">Table of n, a(n) for n = 0..2000</a>
%H A016946 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A016946 a(n) = 36*A002378(n)+9. - _Jean-Bernard François_, Oct 12 2014
%F A016946 From _Wesley Ivan Hurt_, Oct 13 2014: (Start)
%F A016946 G.f.: 9*(1+6*x+x^2)/(1-x)^3.
%F A016946 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
%F A016946 a(n) = A016945(n)^2 = A000290(A016945(n)). (End)
%F A016946 Sum_{n>=0} 1/a(n) = A086729. - _Amiram Eldar_, Nov 16 2020
%F A016946 a(n) = 9*A016754(n). - _R. J. Mathar_, Dec 11 2020
%F A016946 Sum_{n>=0} (-1)^n/a(n) = G/9, where G is Catalan's constant (A006752). - _Amiram Eldar_, Mar 30 2022
%F A016946 E.g.f.: 9*exp(x)*(1 + 8*x + 4*x^2). - _Stefano Spezia_, Aug 19 2022
%p A016946 A016946:=n->(6*n+3)^2: seq(A016946(n), n=0..50); # _Wesley Ivan Hurt_, Oct 13 2014
%t A016946 (6 Range[0, 50] + 3)^2 (* or *)
%t A016946 CoefficientList[Series[9 (1 + 6 x + x^2)/(1 - x)^3, {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Oct 13 2014 *)
%t A016946 LinearRecurrence[{3,-3,1},{9,81,225},40] (* _Harvey P. Dale_, Jul 13 2015 *)
%o A016946 (Magma) [(6*n+3)^2: n in [0..60]]; // _Vincenzo Librandi_, May 05 2011
%o A016946 (PARI) a(n)=(6*n+3)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A016946 Cf. A000290, A002378, A006752, A016754, A016945, A086729.
%K A016946 nonn,easy
%O A016946 0,1
%A A016946 _N. J. A. Sloane_