A011861 a(n) = floor(n(n-1)/8).

0, 0, 0, 0, 1, 2, 3, 5, 7, 9, 11, 13, 16, 19, 22, 26, 30, 34, 38, 42, 47, 52, 57, 63, 69, 75, 81, 87, 94, 101, 108, 116, 124, 132, 140, 148, 157, 166, 175, 185, 195, 205, 215, 225, 236, 247, 258, 270, 282, 294, 306, 318, 331, 344, 357, 371, 385, 399, 413, 427, 442, 457, 472

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Matthew House, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3, -4, 4, -4, 4, -4, 4, -3, 1).

Programs

Magma

[n*(n-1) div 8: n in [0..70]]; // Vincenzo Librandi, Aug 08 2015

Maple

seq(floor(binomial(n,2)/4), n=0..51); # Zerinvary Lajos, Jan 12 2009

Mathematica

LinearRecurrence[{3, -4, 4, -4, 4, -4, 4, -3, 1}, {0, 0, 0, 0, 1, 2, 3, 5, 7}, 70] (* Vincenzo Librandi, Aug 08 2015 *)

Formula

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

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

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