A100451 a(n) = 0 for n <= 2; for n >= 3, a(n) = (n-2)*floor((n^2-2)/(n-2)).

0, 0, 7, 14, 21, 32, 45, 60, 77, 96, 117, 140, 165, 192, 221, 252, 285, 320, 357, 396, 437, 480, 525, 572, 621, 672, 725, 780, 837, 896, 957, 1020, 1085, 1152, 1221, 1292, 1365, 1440, 1517, 1596, 1677, 1760, 1845, 1932, 2021, 2112, 2205, 2300, 2397, 2496, 2597, 2700

Offset: 1

Author

N. J. A. Sloane, Nov 22 2004

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Third row of array in A100452.

Cf. A028347.

Programs

Magma

[0, 0] cat [(n-2)*Floor((n^2-2)/(n-2)): n in [3..30]]; // Vincenzo Librandi, Oct 04 2011

Mathematica

Join[{0,0,7,14},Table[(n-2)(n+2),{n,5,60}]] (* or *) Join[{0,0,7,14}, LinearRecurrence[{3,-3,1},{21,32,45},60]] (* Harvey P. Dale, Oct 03 2011 *)

PARI

a(n)=if(n<3,0,(n^2-2)\(n-2)*(n-2)) \\ Charles R Greathouse IV, Oct 16 2015

SageMath

def A100451(n):
    return 7 * (n - 2) * ((n - 1) // 2) if n < 5 else (n - 2) * (n + 2)
print([A100451(n) for n in range(1, 61)])  # G. C. Greubel, Apr 07 2023

Formula

a(n) = (n-2)*(n+2), n >= 5. - R. J. Mathar, Aug 17 2009

a(n) = A028347(n), n >= 5. - R. J. Mathar, Jul 31 2010

Extensions

Factor in definition corrected by R. J. Mathar, Aug 17 2009