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%I #39 Feb 27 2024 11:51:20
%S 8,10,16,26,40,58,80,106,136,170,208,250,296,346,400,458,520,586,656,
%T 730,808,890,976,1066,1160,1258,1360,1466,1576,1690,1808,1930,2056,
%U 2186,2320,2458,2600,2746,2896,3050,3208,3370,3536,3706,3880,4058
%N a(n) = 2*n^2 + 8.
%C The identity (n^3+4*n)^2 + (2*n^2+8)^2 = (n^2+4)^3 can be written as A155965(n)^2 + a(n)^2 = A087475(n)^3.
%H Vincenzo Librandi, <a href="/A155966/b155966.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 G.f.: 2*(4 - 7*x + 5*x^2)/(1 - x)^3.
%F a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F a(n) = 2*A087475(n). - _Bruno Berselli_, Mar 13 2015
%F From _Amiram Eldar_, Feb 25 2023: (Start)
%F Sum_{n>=0} 1/a(n) = 1/16 + coth(2*Pi)*Pi/8.
%F Sum_{n>=0} (-1)^n/a(n) = 1/16 + cosech(2*Pi)*Pi/8. (End)
%t LinearRecurrence[{3, -3, 1}, {8, 10, 16}, 50] (* _Vincenzo Librandi_, Feb 22 2012 *)
%t 2*Range[0,50]^2+8 (* _Harvey P. Dale_, Mar 01 2018 *)
%o (PARI) a(n)=2*n^2+8 \\ _Charles R Greathouse IV_, Jan 11 2012
%o (Magma) [2*n^2+8: n in [0..50]]; // _Vincenzo Librandi_, Feb 22 2012
%Y Cf. A087475, A155965.
%Y Cf. similar sequences listed in A255843.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Jan 31 2009
%E Offset changed from 1 to 0 and added a(0)=8 by _Bruno Berselli_, Mar 13 2015
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