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A136016 a(n) = 9*n^2-1.

%I A136016 #54 Jun 19 2025 22:42:43
%S A136016 8,35,80,143,224,323,440,575,728,899,1088,1295,1520,1763,2024,2303,
%T A136016 2600,2915,3248,3599,3968,4355,4760,5183,5624,6083,6560,7055,7568,
%U A136016 8099,8648,9215,9800,10403,11024,11663,12320,12995,13688,14399,15128,15875,16640
%N A136016 a(n) = 9*n^2-1.
%H A136016 Vincenzo Librandi, <a href="/A136016/b136016.txt">Table of n, a(n) for n = 1..3000</a>
%H A136016 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A136016 a(n) = A005563(3*n-1). - _Paul Curtz_, Oct 28 2008
%F A136016 a(2*n) = A136017(n). - _Paul Curtz_, Sep 30 2008
%F A136016 a(n) = A016777(n)*A016789(n-1). - _Reinhard Zumkeller_, Feb 15 2009
%F A136016 G.f.: x*(-8-11*x+x^2) / ( x-1 )^3. - _R. J. Mathar_, Jul 01 2011
%F A136016 From _Amiram Eldar_, Jul 31 2020: (Start)
%F A136016 Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/18.
%F A136016 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/9 - 1/2. (End)
%F A136016 From _Amiram Eldar_, Feb 04 2021: (Start)
%F A136016 Product_{n>=1} (1 + 1/a(n)) = 2*Pi/(3*sqrt(3)) (A248897).
%F A136016 Product_{n>=1} (1 - 1/a(n)) = sqrt(2/3)*sin(sqrt(2)*Pi/3). (End)
%F A136016 a(n) = a(-n) for all n in Z. Sum_{n in Z} 1/a(n) = -Pi/3^(3/2) = -A073010. - _Michael Somos_, May 21 2023
%F A136016 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Wesley Ivan Hurt_, Jun 19 2025
%t A136016 Table[9n^2 - 1, {n, 1, 100}]
%t A136016 LinearRecurrence[{3,-3,1},{8,35,80},50] (* _Harvey P. Dale_, Oct 09 2012 *)
%o A136016 (Magma) [9*n^2-1: n in [1..50]]; // _Vincenzo Librandi_, May 09 2011
%o A136016 (PARI) a(n)=9*n^2-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A136016 Cf. A001359, A006512, A037074, A248897.
%Y A136016 Cf. A005563, A016777, A016789, A073010, A136017.
%K A136016 nonn,easy
%O A136016 1,1
%A A136016 _Artur Jasinski_, Dec 10 2007