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

4, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027

Offset: 1

Author

Vincenzo Librandi, Oct 20 2011

Keywords

• nonn
• easy
• less

Comments

Shifted variant of A102305. - R. J. Mathar, Oct 20 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A059100, A102305, A183199, A160842, A010000.

Programs

Magma

[Round((n+1/n)^2): n in [1..60]];

Mathematica

Table[Floor[(n+1/n)^2+1/2],{n,50}] (* Harvey P. Dale, Aug 12 2012 *)
Join[{4}, 2+Range[2,50]^2] (* G. C. Greubel, Feb 04 2024 *)

SageMath

[4]+[n^2+2 for n in range(2,51)] # G. C. Greubel, Feb 04 2024

Formula

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

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

From G. C. Greubel, Feb 04 2024: (Start)

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

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. - Chai Wah Wu, May 09 2024