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Floor( 7*n^2/2 ).
1

%I #19 Sep 08 2022 08:44:51

%S 0,3,14,31,56,87,126,171,224,283,350,423,504,591,686,787,896,1011,

%T 1134,1263,1400,1543,1694,1851,2016,2187,2366,2551,2744,2943,3150,

%U 3363,3584,3811,4046,4287,4536,4791,5054,5323,5600,5883,6174,6471,6776,7087,7406,7731

%N Floor( 7*n^2/2 ).

%H Vincenzo Librandi, <a href="/A032525/b032525.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 (2,0,-2,1).

%F a(n) = (-1+(-1)^n+14*n^2)/4. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: -x*(3*x^2+8*x+3) / ((x-1)^3*(x+1)). - _Colin Barker_, Aug 03 2013

%t CoefficientList[Series[- x (3 x^2 + 8 x + 3) / ((x - 1)^3 (x + 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 04 2013 *)

%t Floor[7*Range[0,50]^2/2] (* or *) LinearRecurrence[{2,0,-2,1},{0,3,14,31},50] (* _Harvey P. Dale_, Aug 22 2020 *)

%o (Magma) [Floor(7*n^2/2): n in [0..50]]; // _Vincenzo Librandi_, Aug 04 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Aug 03 2013