A008130 a(n) = floor(n/3)*ceiling(n/3).

0, 0, 0, 1, 2, 2, 4, 6, 6, 9, 12, 12, 16, 20, 20, 25, 30, 30, 36, 42, 42, 49, 56, 56, 64, 72, 72, 81, 90, 90, 100, 110, 110, 121, 132, 132, 144, 156, 156, 169, 182, 182, 196, 210, 210, 225, 240, 240, 256, 272, 272, 289, 306, 306, 324, 342, 342, 361, 380, 380, 400

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Crossrefs

Cf. A002264, A072691.

Programs

Magma

[Floor(n/3)*Ceiling(n/3): n in [0..60]]; // Vincenzo Librandi, Jun 10 2013

Maple

A008130:=n->ceil(n/3)*floor(n/3); seq(A008130(n), n=0..60); # Wesley Ivan Hurt, Feb 01 2014

Mathematica

f[n_]:=Ceiling[n/3]*Floor[n/3];Table[f[n],{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 01 2010 *)
CoefficientList[Series[- x^3 (1 + x) / ((1 + x + x^2)^2 (x - 1)^3), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 10 2013 *)
LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,0,1,2,2,4},60] (* Harvey P. Dale, Dec 31 2016 *)

Formula

From R. J. Mathar, Jan 27 2011: (Start)

a(n) = A002264(n)*A002264(n+2).

G.f. -x^3*(1+x) / ( (1+x+x^2)^2*(x-1)^3 ). (End)

From Amiram Eldar, May 10 2025: (Start)

Sum_{n>=3} 1/a(n) = 2 + Pi^2/6.

Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/12 (A072691). (End)