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%I #15 Sep 08 2022 08:44:43
%S 100,484,1156,2116,3364,4900,6724,8836,11236,13924,16900,20164,23716,
%T 27556,31684,36100,40804,45796,51076,56644,62500,68644,75076,81796,
%U 88804,96100,103684,111556,119716
%N a(n) = (12*n+10)^2.
%H Harvey P. Dale, <a href="/A017642/b017642.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 From _Wesley Ivan Hurt_, Dec 22 2020: (Start)
%F G.f.: 4*(25 + 46*x + x^2)/(1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3.
%F a(n) = 144*n^2 + 240*n + 100.
%F a(n) = A017641(n)^2. (End)
%e a(5) = (12*5+10)^2 = 70^2 = 4900.
%t (12*Range[0,30]+10)^2 (* or *) LinearRecurrence[{3,-3,1},{100,484,1156},30] (* _Harvey P. Dale_, May 08 2017 *)
%t CoefficientList[Series[4*(25 + 46 x + x^2)/(1 - x)^3, {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Dec 22 2020 *)
%o (PARI) a(n)=(12*n+10)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Magma) [(12*n+10)^2 : n in [0..40]]; // _Wesley Ivan Hurt_, Dec 22 2020
%Y Cf. A016969, A016970, A017641, A017643.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
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