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

1,1

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).

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)

Mathematica

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

Prog

(Magma) [Floor((n+1/n)^4): n in [1..60]];
(PARI) a(n)=floor((n+1/n)^4) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A010000, A014052.

Sequence in context: A347410 A253152 A305362 * A144448 A070584 A205072

Adjacent sequences: A197600 A197601 A197602 * A197604 A197605 A197606

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 17 2011

Status

approved