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%I #50 May 22 2023 08:57:54
%S 8,35,80,143,224,323,440,575,728,899,1088,1295,1520,1763,2024,2303,
%T 2600,2915,3248,3599,3968,4355,4760,5183,5624,6083,6560,7055,7568,
%U 8099,8648,9215,9800,10403,11024,11663,12320,12995,13688,14399,15128,15875,16640
%N a(n) = 9*n^2-1.
%H Vincenzo Librandi, <a href="/A136016/b136016.txt">Table of n, a(n) for n = 1..3000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A005563(3*n-1). - _Paul Curtz_, Oct 28 2008
%F a(2*n) = A136017(n). - _Paul Curtz_, Sep 30 2008
%F a(n) = A016777(n)*A016789(n-1). - _Reinhard Zumkeller_, Feb 15 2009
%F G.f.: x*(-8-11*x+x^2) / ( x-1 )^3 . - _R. J. Mathar_, Jul 01 2011
%F From _Amiram Eldar_, Jul 31 2020: (Start)
%F Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/18.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/9 - 1/2. (End)
%F From _Amiram Eldar_, Feb 04 2021: (Start)
%F Product_{n>=1} (1 + 1/a(n)) = 2*Pi/(3*sqrt(3)) (A248897).
%F Product_{n>=1} (1 - 1/a(n)) = sqrt(2/3)*sin(sqrt(2)*Pi/3). (End)
%F 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
%t Table[9n^2 - 1, {n, 1, 100}]
%t LinearRecurrence[{3,-3,1},{8,35,80},50] (* _Harvey P. Dale_, Oct 09 2012 *)
%o (Magma) [9*n^2-1: n in [1..50]]; // _Vincenzo Librandi_, May 09 2011
%o (PARI) a(n)=9*n^2-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A001359, A006512, A037074, A248897.
%Y Cf. A005563, A016777, A016789, A073010, A136017.
%K nonn,easy
%O 1,1
%A _Artur Jasinski_, Dec 10 2007
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