A197904 a(n) = ceiling((n+1/n)^5).

32, 98, 412, 1387, 3803, 8918, 18594, 35410, 62786, 105102, 167817, 257593, 382409, 551685, 776401, 1069217, 1444593, 1918909, 2510585, 3240201, 4130617, 5207093, 6497409, 8031985, 9844001, 11969517, 14447593, 17320409, 20633385, 24435301, 28778417, 33718593

Offset: 1

Author

Vincenzo Librandi, Oct 19 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 (6,-15,20,-15,6,-1).

Crossrefs

Cf. A014058.

Programs

Magma

[Ceiling((n+1/n)^5): n in [1..50]]

Maple

A197904:=n->ceil((n+1/n)^5): seq(A197904(n), n=1..40); # Wesley Ivan Hurt, Apr 23 2017

Mathematica

Table[Ceiling[(n+1/n)^5],{n,50}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{32,98,412,1387,3803,8918,18594,35410,62786,105102,167817,257593,382409,551685,776401,1069217},40] (* Harvey P. Dale, Jul 10 2021 *)

PARI

a(n)=ceil((n+1/n)^5) \\ Charles R Greathouse IV, Nov 21 2011

Formula

a(n) = n^5 + 5n^3 + 10n for n > 10. [Charles R Greathouse IV, Nov 21 2011]

G.f.: (167817 - 749309 x + 1354106 x^2 - 1235214 x^3 + 567821 x^4 -

105101 x^5)/(-1 + x)^6 - Harvey P. Dale, Jul 10 2021