A100451 - OEIS

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

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OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

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 *)

PROG

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

CROSSREFS

Third row of array in A100452.

Cf. A028347.

Sequence in context: A033004 A189931 A164005 * A028555 A061823 A018890

Adjacent sequences: A100448 A100449 A100450 * A100452 A100453 A100454