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Nearest integer to 1/(Sum_{k>=n} 1/k^4).
1

%I #29 Apr 20 2021 11:52:38

%S 1,12,50,134,280,507,834,1277,1855,2586,3489,4580,5878,7401,9168,

%T 11195,13501,16104,19023,22274,25876,29847,34206,38969,44155,49782,

%U 55869,62432,69490,77061,85164,93815,103033,112836,123243,134270,145936

%N Nearest integer to 1/(Sum_{k>=n} 1/k^4).

%H Harvey P. Dale, <a href="/A083559/b083559.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).

%F a(n) = floor(3*n^3-9/2*n^2+15/4*n-3/4) for n > 3.

%F G.f.: -x*(x^9-3*x^8+3*x^7-2*x^6-10*x^5-15*x^4-19*x^3-17*x^2-9*x-1) / ((x-1)^4*(x+1)*(x^2+1)). - _Colin Barker_, Dec 01 2012

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7). - _Wesley Ivan Hurt_, Apr 20 2021

%t LinearRecurrence[{3,-3,1,1,-3,3,-1},{1,12,50,134,280,507,834,1277,1855,2586},40] (* _Harvey P. Dale_, Sep 18 2018 *)

%o (PARI) a(n)=round(1/(zeta(4)-sum(k=1,n-1,1/k^4)))

%Y Cf. A001844.

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Jun 12 2003