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%I #23 Jun 17 2017 02:59:15
%S -4,-1,2,13,40,91,174,297,468,695,986,1349,1792,2323,2950,3681,4524,
%T 5487,6578,7805,9176,10699,12382,14233,16260,18471,20874,23477,26288,
%U 29315,32566,36049,39772,43743,47970,52461,57224,62267,67598,73225,79156,85399
%N Values of Newton-Gregory forward interpolating polynomial (1/3)*(2*n - 3)*(2*n^2 - 3*n + 4).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) - A177342(n-1) = (n-1)^2, with n>1. For n=6, a(6) - A177342(5) = 174 - 149 = 5^2. - _Bruno Berselli_, May 23 2010
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Colin Barker_, May 18 2014
%F G.f.: (15*x^3-18*x^2+15*x-4) / (x-1)^4. - _Colin Barker_, May 18 2014
%F a(n) = A059259(2*n,3), n>1. - _Mathew Englander_, May 17 2014
%t LinearRecurrence[{4,-6,4,-1},{-4,-1,2,13},50] (* _Harvey P. Dale_, Apr 20 2015 *)
%o (PARI) a(n) = (1/3)*(2*n-3)*(2*n^2-3*n+4); \\ _Michel Marcus_, May 18 2014
%Y Equals A030434 shifted left twice.
%K sign,easy
%O 0,1
%A Ilias.Kotsireas(AT)lip6.fr (Ilias Kotsireas)
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