%I #24 Aug 23 2017 23:39:43
%S 0,13,51,114,202,315,453,616,804,1017,1255,1518,1806,2119,2457,2820,
%T 3208,3621,4059,4522,5010,5523,6061,6624,7212,7825,8463,9126,9814,
%U 10527,11265,12028,12816,13629,14467
%N a(n) = n*(25*n + 1)/2.
%H G. C. Greubel, <a href="/A022283/b022283.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + 25*n - 12 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010
%F a(0)=0, a(1)=13, a(2)=51; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 04 2014
%F a(n) = A000217(13*n) - A000217(12*n). - _Bruno Berselli_, Oct 13 2016
%F From _G. C. Greubel_, Aug 23 2017: (Start)
%F G.f.: x*(12*x + 13)/(1-x)^3.
%F E.g.f.: (x/2)*(25*x + 26)*exp(x). (End)
%t Table[n/2 (25 n + 1), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 13, 51}, 40] (* _Harvey P. Dale_, May 04 2014 *)
%o (PARI) a(n)=n*(25*n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. similar sequences listed in A022289.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_