cp's OEIS Frontend

A017390 a(n) = (11*n)^2.

%I A017390 #22 Dec 01 2024 10:05:22
%S A017390 0,121,484,1089,1936,3025,4356,5929,7744,9801,12100,14641,17424,20449,
%T A017390 23716,27225,30976,34969,39204,43681,48400,53361,58564,64009,69696,
%U A017390 75625,81796,88209,94864,101761,108900,116281,123904,131769,139876,148225,156816,165649,174724
%N A017390 a(n) = (11*n)^2.
%H A017390 Vincenzo Librandi, <a href="/A017390/b017390.txt">Table of n, a(n) for n = 0..10000</a>
%H A017390 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A017390 From _Amiram Eldar_, Jan 25 2021: (Start)
%F A017390 Sum_{n>=1} 1/a(n) = Pi^2/726.
%F A017390 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1452.
%F A017390 Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/11)/(Pi/11).
%F A017390 Product_{n>=1} (1 - 1/a(n)) = sin(Pi/11)/(Pi/11). (End)
%F A017390 G.f.: -((121*x*(1+x))/(-1+x)^3). - _Harvey P. Dale_, Nov 04 2021
%F A017390 From _Elmo R. Oliveira_, Nov 30 2024: (Start)
%F A017390 E.g.f.: 121*x*(1 + x)*exp(x).
%F A017390 a(n) = 121*A000290(n) = A008593(n)^2.
%F A017390 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A017390 (11 Range[0,30])^2 (* or *) LinearRecurrence[{3,-3,1},{0,121,484},30] (* _Harvey P. Dale_, Nov 04 2021 *)
%o A017390 (Magma) [(11*n)^2: n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2011
%o A017390 (PARI) a(n)=(11*n)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A017390 Cf. A000290, A008593.
%K A017390 nonn,easy
%O A017390 0,2
%A A017390 _N. J. A. Sloane_