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A197985 a(n) = round((n+1/n)^2).

%I A197985 #29 Mar 17 2025 14:57:07
%S A197985 4,6,11,18,27,38,51,66,83,102,123,146,171,198,227,258,291,326,363,402,
%T A197985 443,486,531,578,627,678,731,786,843,902,963,1026,1091,1158,1227,1298,
%U A197985 1371,1446,1523,1602,1683,1766,1851,1938,2027
%N A197985 a(n) = round((n+1/n)^2).
%C A197985 Shifted variant of A102305. - _R. J. Mathar_, Oct 20 2011
%H A197985 Vincenzo Librandi, <a href="/A197985/b197985.txt">Table of n, a(n) for n = 1..10000</a>
%H A197985 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A197985 a(n) = n^2 + 2, n > 1.
%F A197985 a(n) = a(n-1) + 2*n - 1, n > 2.
%F A197985 From _G. C. Greubel_, Feb 04 2024: (Start)
%F A197985 G.f.: x*(4 - 6*x + 5*x^2 - x^3)/(1 - x)^3.
%F A197985 E.g.f.: -2 + x + (2 + x + x^2)*exp(x). (End)
%F A197985 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. - _Chai Wah Wu_, May 09 2024
%t A197985 Table[Floor[(n+1/n)^2+1/2],{n,50}] (* _Harvey P. Dale_, Aug 12 2012 *)
%t A197985 Join[{4}, 2+Range[2,50]^2] (* _G. C. Greubel_, Feb 04 2024 *)
%o A197985 (Magma) [Round((n+1/n)^2): n in [1..60]];
%o A197985 (SageMath) [4]+[n^2+2 for n in range(2,51)] # _G. C. Greubel_, Feb 04 2024
%Y A197985 Cf. A059100, A102305, A183199, A160842, A010000.
%K A197985 nonn,easy,less
%O A197985 1,1
%A A197985 _Vincenzo Librandi_, Oct 20 2011