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

%I #22 Dec 01 2024 10:05:22

%S 0,121,484,1089,1936,3025,4356,5929,7744,9801,12100,14641,17424,20449,

%T 23716,27225,30976,34969,39204,43681,48400,53361,58564,64009,69696,

%U 75625,81796,88209,94864,101761,108900,116281,123904,131769,139876,148225,156816,165649,174724

%N a(n) = (11*n)^2.

%H Vincenzo Librandi, <a href="/A017390/b017390.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _Amiram Eldar_, Jan 25 2021: (Start)

%F Sum_{n>=1} 1/a(n) = Pi^2/726.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1452.

%F Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/11)/(Pi/11).

%F Product_{n>=1} (1 - 1/a(n)) = sin(Pi/11)/(Pi/11). (End)

%F G.f.: -((121*x*(1+x))/(-1+x)^3). - _Harvey P. Dale_, Nov 04 2021

%F From _Elmo R. Oliveira_, Nov 30 2024: (Start)

%F E.g.f.: 121*x*(1 + x)*exp(x).

%F a(n) = 121*A000290(n) = A008593(n)^2.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

%t (11 Range[0,30])^2 (* or *) LinearRecurrence[{3,-3,1},{0,121,484},30] (* _Harvey P. Dale_, Nov 04 2021 *)

%o (Magma) [(11*n)^2: n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2011

%o (PARI) a(n)=(11*n)^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000290, A008593.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_