A017414 - OEIS

%I #18 Sep 08 2022 08:44:42

%S 4,169,576,1225,2116,3249,4624,6241,8100,10201,12544,15129,17956,

%T 21025,24336,27889,31684,35721,40000,44521,49284,54289,59536,65025,

%U 70756,76729,82944,89401,96100,103041

%N (11n+2)^2.

%H Vincenzo Librandi, <a href="/A017414/b017414.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: (4+157*x+81*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jul 07 2012

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 07 2012

%t CoefficientList[Series[(4+157*x+81*x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)

%o (Magma) I:=[4, 169, 576]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jul 07 2012

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

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.