A197604 a(n) = floor((n+1/n)^5).

32, 97, 411, 1386, 3802, 8917, 18593, 35409, 62785, 105101, 167816, 257592, 382408, 551684, 776400, 1069216, 1444592, 1918908, 2510584, 3240200, 4130616, 5207092, 6497408, 8031984, 9844000, 11969516, 14447592, 17320408, 20633384, 24435300, 28778416, 33718592, 39315408, 45632284, 52736600, 60699816, 69597592, 79509908

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 (6,-15,20,-15,6,-1).

Crossrefs

Cf. A014052.

Programs

Magma

[Floor((n+1/n)^5): n in [1..60]]

Mathematica

Join[{32,97,411,1386,3802,8917,18593,35409,62785,105101},LinearRecurrence[{6,-15,20,-15,6,-1},{167816,257592,382408,551684,776400,1069216},30]] (* Harvey P. Dale, Jan 16 2015 *)

PARI

a(n)=floor((n+1/n)^5) \\ Charles R Greathouse IV, Oct 27 2011

Formula

From Bruno Berselli, Oct 27 2011: (Start)

G.f.: x*(32-95*x+309*x^2-265*x^3+191*x^4-62*x^5+16*x^6-13*x^7+11*x^8-5*x^9+5*x^11-10*x^12+10*x^13-5*x^14+x^15)/(1-x)^6.

a(n) = n*(n^4+5*n^2+10) + A033330(n) for n>1.

a(n) = A197904(n) - 1 for n>1. (End)