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A197605 Floor( ( n + 1/n )^6 ). 2

%I

%S 64,244,1371,5892,19770,54992,132810,287700,572042,1061520,1861242,

%T 3112580,5000730,7762992,11697770,17174292,24643050,34646960,47833242,

%U 64966020,86939642,114792720,149722890,193102292,246493770,311667792,390620090,485590020

%N Floor( ( n + 1/n )^6 ).

%H Vincenzo Librandi, <a href="/A197605/b197605.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

%F 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

%t Table[Floor[(n + 1/n)^6], {n, 40}] (* _T. D. Noe_, Dec 27 2011 *)

%t 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 *)

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

%o (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

%Y Cf. A014052, A197602, A197603, A197604.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Oct 18 2011

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Last modified January 16 18:07 EST 2022. Contains 350376 sequences. (Running on oeis4.)