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a(n) = 4*n^5 + 10*n^4 + 13*n^3 + 11*n^2 + 5*n + 1.
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%I #20 Oct 23 2021 13:32:46

%S 1,44,447,2248,7685,20676,47299,96272,179433,312220,514151,809304,

%T 1226797,1801268,2573355,3590176,4905809,6581772,8687503,11300840,

%U 14508501,18406564,23100947,28707888,35354425,43178876,52331319

%N a(n) = 4*n^5 + 10*n^4 + 13*n^3 + 11*n^2 + 5*n + 1.

%C Let x(n) = (1/2)*(-(2*n+1) + sqrt((2*n+1)^2 + 4)) and f(k) = (-1)*(Sum_{i=1..k} Sum_{j=1..i} (-1)^floor(j*x(n))), then a(n) = Max{f(k): 0 < k < A094200(n)}.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F G.f.: (37*x^4 + 206*x^3 + 198*x^2 + 38*x + 1)/(x - 1)^6. - _Jinyuan Wang_, Apr 06 2020

%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,44,447,2248,7685,20676},30] (* _Harvey P. Dale_, Oct 23 2021 *)

%o (PARI) a(n)=4*n^5+10*n^4+13*n^3+11*n^2+5*n+1

%Y Cf. A085005, A094200.

%K nonn,easy

%O 0,2

%A _Benoit Cloitre_, May 25 2004

%E Corrected by _T. D. Noe_, Nov 09 2006