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

%I #20 Feb 05 2024 07:34:23

%S 4,6,11,18,27,38,51,66,83,102,123,146,171,198,227,258,291,326,363,402,

%T 443,486,531,578,627,678,731,786,843,902,963,1026,1091,1158,1227,1298,

%U 1371,1446,1523,1602,1683,1766,1851,1938,2027

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

%C Shifted variant of A102305. - _R. J. Mathar_, Oct 20 2011

%H Vincenzo Librandi, <a href="/A197985/b197985.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n^2 + 2, n > 1.

%F a(n) = a(n-1) + 2*n - 1, n > 2.

%F From _G. C. Greubel_, Feb 04 2024: (Start)

%F G.f.: x*(4 - 6*x + 5*x^2 - x^3)/(1 - x)^3.

%F E.g.f.: -2 + x + (2 + x + x^2)*exp(x). (End)

%t Table[Floor[(n+1/n)^2+1/2],{n,50}] (* _Harvey P. Dale_, Aug 12 2012 *)

%t Join[{4}, 2+Range[2,50]^2] (* _G. C. Greubel_, Feb 04 2024 *)

%o (Magma) [Round((n+1/n)^2): n in [1..60]]

%o (SageMath) [4]+[n^2+2 for n in range(2,51)] # _G. C. Greubel_, Feb 04 2024

%Y Cf. A059100, A102305, A183199.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Oct 20 2011

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)