A011865 a(n) = floor( n*(n - 1)/12 ).

0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 9, 11, 13, 15, 17, 20, 22, 25, 28, 31, 35, 38, 42, 46, 50, 54, 58, 63, 67, 72, 77, 82, 88, 93, 99, 105, 111, 117, 123, 130, 136, 143, 150, 157, 165, 172, 180, 188, 196, 204, 212, 221, 229, 238, 247, 256, 266, 275, 285, 295, 305, 315, 325, 336

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1,-1,2,-1,1,-2,1).

Programs

Maple

seq(floor(binomial(n-1,2)/6), n=1..53); # Zerinvary Lajos, Jan 12 2009

Mathematica

Table[Floor[n*(n - 1)/12], {n, 0, 100}] (* Paolo Xausa, Sep 02 2024 *)

Formula

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = +2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) -a(n-6) +2*a(n-7) -a(n-8) +a(n-9) -2*a(n-10) +a(n-11).

G.f.: x^4*(x^4+1-x^3-x+x^2) / ((1-x)^3*(1+x+x^2)*(x^2+1)*(x^4-x^2+1)). (End)