A171662 a(n) = floor((2*n^2 + n)/6).

0, 0, 1, 3, 6, 9, 13, 17, 22, 28, 35, 42, 50, 58, 67, 77, 88, 99, 111, 123, 136, 150, 165, 180, 196, 212, 229, 247, 266, 285, 305, 325, 346, 368, 391, 414, 438, 462, 487, 513, 540, 567, 595, 623, 652, 682, 713, 744, 776, 808, 841, 875, 910, 945

Offset: 0

Author

Michael Somos, Dec 14 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 1, -2, 1).

Crossrefs

Cf. A078617.

Programs

Magma

[Floor((2*n^2+n)/6): n in [0..60]]; // G. C. Greubel, Sep 25 2018

Mathematica

Table[Floor[(2n^2+n)/6],{n,0,60}] (* or *) LinearRecurrence[{2,-1,0,0,0,1,-2,1},{0,0,1,3,6,9,13,17},60] (* Harvey P. Dale, Oct 15 2014 *)

PARI

{a(n) = (2 * n^2 + n) \ 6};

Formula

a(n) = floor(n*(2*n + 1)/6).

a(n) = A078617(-1 - n) for all n in Z.

a(n) = floor((n+1)/(exp(3/(n+1)) - 1)). - Richard R. Forberg, Jun 22 2013

G.f.: -x^2*(x^4 + x^2 + x + 1)/( (x+1) * (x^2+x+1) * (x^2-x+1) * (x-1)^3). - Alois P. Heinz, Jun 24 2013

a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8); a(0)=0, a(1)=0, a(2)=1, a(3)=3, a(4)=6, a(5)=9, a(6)=13, a(7)=17. - Harvey P. Dale, Oct 15 2014

36*a(n) = 6*n +12*n^2 -11 +3*(-1)^n +2*A061347(n) +6*A057079(n+2). - R. J. Mathar, Apr 26 2022