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 A017522 #33 Dec 06 2024 13:13:37 %S A017522 0,144,576,1296,2304,3600,5184,7056,9216,11664,14400,17424,20736, %T A017522 24336,28224,32400,36864,41616,46656,51984,57600,63504,69696,76176, %U A017522 82944,90000,97344,104976,112896,121104,129600,138384,147456,156816,166464,176400,186624,197136 %N A017522 a(n) = (12*n)^2. %H A017522 Vincenzo Librandi, <a href="/A017522/b017522.txt">Table of n, a(n) for n = 0..1000</a> %H A017522 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A017522 G.f.: 144*x*(1+x)/(1-x)^3. - _Bruno Berselli_, Feb 10 2012 %F A017522 From _Amiram Eldar_, Jan 25 2021: (Start) %F A017522 Sum_{n>=1} 1/a(n) = Pi^2/864. %F A017522 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1728. %F A017522 Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/12)/(Pi/12). %F A017522 Product_{n>=1} (1 - 1/a(n)) = sin(Pi/12)/(Pi/12) = 3*sqrt(2)*(sqrt(3)-1)/Pi. (End) %F A017522 From _Elmo R. Oliveira_, Dec 02 2024: (Start) %F A017522 E.g.f.: 144*x*(1 + x)*exp(x). %F A017522 a(n) = 144*A000290(n) = A008594(n)^2 = A000290(A008594(n)). %F A017522 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End) %t A017522 LinearRecurrence[{3, -3, 1}, {0, 144, 576}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *) %t A017522 (12 Range[0, 30])^2 (* _Bruno Berselli_, Feb 10 2012 *) %o A017522 (Magma) [(12*n)^2: n in [0..35]]; // _Vincenzo Librandi_, Feb 10 2012 %o A017522 (PARI) a(n)=(12*n)^2 \\ _Charles R Greathouse IV_, Jun 17 2017 %Y A017522 Cf. A000290 (n^2), A008594 (12*n). %K A017522 nonn,easy %O A017522 0,2 %A A017522 _N. J. A. Sloane_