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a(n) = (5/6)*n^3+(5/2)*n^2+(8/3)*n.
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%I #15 Oct 18 2022 15:13:41

%S 0,6,22,53,104,180,286,427,608,834,1110,1441,1832,2288,2814,3415,4096,

%T 4862,5718,6669,7720,8876,10142,11523,13024,14650,16406,18297,20328,

%U 22504,24830,27311,29952,32758,35734,38885,42216,45732,49438,53339,57440,61746,66262

%N a(n) = (5/6)*n^3+(5/2)*n^2+(8/3)*n.

%H Harvey P. Dale, <a href="/A092185/b092185.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n)= +4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). G.f.: x*(6-2*x+x^2)/(x-1)^4. - _R. J. Mathar_, Jun 21 2010

%t LinearRecurrence[{4,-6,4,-1},{0,6,22,53},50] (* _Harvey P. Dale_, May 27 2012 *)

%o (PARI) a(n)=(5/6)*n^3+(5/2)*n^2+(8/3)*n \\ _Charles R Greathouse IV_, Oct 18 2022

%Y Partial sums of A005891.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Apr 02 2004