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%I #14 Jun 17 2017 02:59:31
%S 5,7,13,25,45,75,117,173,245,335,445,577,733,915,1125,1365,1637,1943,
%T 2285,2665,3085,3547,4053,4605,5205,5855,6557,7313,8125,8995,9925,
%U 10917,11973,13095,14285,15545,16877,18283,19765,21325,22965
%N (n^3 - n + 15)/3.
%H B. Berselli, <a href="/A155757/b155757.txt">Table of n, a(n) for n = 1..10000</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)=n(n-1)+a(n-1), with a(1)=5.
%F a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) = 5+n(n^2-1)/3 = 5+A007290(n+1). G.f.: x(5-13x+15x^2-5x^3)/(1-x)^4. [From _R. J. Mathar_, Feb 19 2009]
%t RecurrenceTable[{a[1]==5,a[n]==n(n-1)+a[n-1]},a[n],{n,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{5,7,13,25},50] (* _Harvey P. Dale_, Jun 29 2011 *)
%o (PARI) a(n)=(n^3-n)/3+5 \\ _Charles R Greathouse IV_, Jan 11 2012
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 26 2009
%E New name from _Charles R Greathouse IV_, Jan 11 2012
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