A197603 a(n) = floor((n+1/n)^4).

16, 39, 123, 326, 731, 1446, 2603, 4358, 6891, 10406, 15131, 21318, 29243, 39206, 51531, 66566, 84683, 106278, 131771, 161606, 196251, 236198, 281963, 334086, 393131, 459686, 534363, 617798, 710651, 813606, 927371, 1052678, 1190283, 1340966, 1505531, 1684806, 1879643, 2090918, 2319531, 2566406, 2832491, 3118758

Offset: 1

Author

Vincenzo Librandi, Oct 17 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A010000, A014052.

Programs

Magma

[Floor((n+1/n)^4): n in [1..60]];

Mathematica

Table[Floor[(n+1/n)^4],{n,50}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{16,39,123,326,731,1446,2603},50] (* Harvey P. Dale, Jun 03 2015 *)

PARI

a(n)=floor((n+1/n)^4) \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Bruno Berselli, Oct 17 2011: (Start)

G.f.: x*(16-41*x+88*x^2-59*x^3+21*x^4-x^6)/(1-x)^5.

a(n) = (n^2+2)^2+2 for n>2, a(1)=16, a(2)=39.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n=6 and n>7.

a(n) = A010000(A010000(n)) for n>2. (End)