A032525 Floor( 7*n^2/2 ).

0, 3, 14, 31, 56, 87, 126, 171, 224, 283, 350, 423, 504, 591, 686, 787, 896, 1011, 1134, 1263, 1400, 1543, 1694, 1851, 2016, 2187, 2366, 2551, 2744, 2943, 3150, 3363, 3584, 3811, 4046, 4287, 4536, 4791, 5054, 5323, 5600, 5883, 6174, 6471, 6776, 7087, 7406, 7731

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

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

Mathematica

CoefficientList[Series[- x (3 x^2 + 8 x + 3) / ((x - 1)^3 (x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 04 2013 *)
Floor[7*Range[0, 50]^2/2] (* or *) LinearRecurrence[{2, 0, -2, 1}, {0, 3, 14, 31}, 50] (* Harvey P. Dale, Aug 22 2020 *)

Prog

(Magma) [Floor(7*n^2/2): n in [0..50]]; // Vincenzo Librandi, Aug 04 2013

Crossrefs

Sequence in context: A235137 A197944 A071396 * A294420 A197946 A130697

Adjacent sequences: A032522 A032523 A032524 * A032526 A032527 A032528

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Aug 03 2013

Status

approved