A197605 Floor( ( n + 1/n )^6 ).

64, 244, 1371, 5892, 19770, 54992, 132810, 287700, 572042, 1061520, 1861242, 3112580, 5000730, 7762992, 11697770, 17174292, 24643050, 34646960, 47833242, 64966020, 86939642, 114792720, 149722890, 193102292, 246493770, 311667792, 390620090, 485590020

Offset: 1

Author

Vincenzo Librandi, Oct 18 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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A014052, A197602, A197603, A197604.

Programs

Magma

[Floor((n+1/n)^6): n in [1..40]]

Mathematica

Table[Floor[(n + 1/n)^6], {n, 40}] (* T. D. Noe, Dec 27 2011 *)
CoefficientList[Series[(64 - 204 x + 1007 x^2 - 821 x^3 + 1017 x^4 - 455 x^5 + 125 x^6 - 15 x^7 + 3 x^8 - x^9) / (1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2014 *)

PARI

a(n)=if(n>3,n^6+6*n^4+15*n^2+20,[64,244,1371][n]) \\ Charles R Greathouse IV, Dec 27 2011

Formula

For n > 3, a(n) = n^6 + 6n^4 + 15n^2 + 20. [Charles R Greathouse IV, Dec 27 2011]

G.f.: x*(64-204*x+1007*x^2-821*x^3+1017*x^4-455*x^5+125*x^6-15*x^7+3*x^8-x^9)/(1-x)^7. - Vincenzo Librandi, Dec 18 2014