A082667 a(n) = floor(2n/3) * ceiling(2n/3) / 2.

0, 1, 2, 3, 6, 8, 10, 15, 18, 21, 28, 32, 36, 45, 50, 55, 66, 72, 78, 91, 98, 105, 120, 128, 136, 153, 162, 171, 190, 200, 210, 231, 242, 253, 276, 288, 300, 325, 338, 351, 378, 392, 406, 435, 450, 465, 496, 512, 528, 561, 578, 595, 630, 648, 666, 703, 722, 741

Offset

1,3

Comments

Prefixing A082667 by 0,0,0 gives the sequence c(n) defined as the number of (x,y,z) satisfying 2w = 3x-3y where w,x,y are all in {1,...,n}, for n>=0; see the Formula section.

For n >= 2, numbers k such that floor(sqrt(2k)+1/2) | 2k. - Wesley Ivan Hurt, Dec 01 2020

Links

Table of n, a(n) for n=1..58.

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Formula

a(n) = a(n-1) + 2a(n-3) - 2a(n-4) - a(n-6) + a(n-7), (with 0,0,0 prefixed as in the Comments section). - Clark Kimberling, Apr 15 2012

a(n) = floor((n + 1)/3)*(n - floor((n + 1)/3)). - Wesley Ivan Hurt, Jun 06 2014

G.f.: -x^2*(1+x)*(1+x^2) / ( (1+x+x^2)^2*(x-1)^3 ). - R. J. Mathar, Jun 07 2014

Mathematica

n2[n_]:=Module[{c=2*n/3}, (Floor[c]Ceiling[c])/2]; Array[n2, 60] (* Harvey P. Dale, Feb 03 2012 *)
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {0, 1, 2, 3, 6, 8, 10}, 60] (* Robert G. Wilson v, Jun 06 2014 *)

Crossrefs

Cf. A008130, A151842 (first differences).

Sequence in context: A181486 A179785 A246445 * A098162 A076627 A020489

Adjacent sequences: A082664 A082665 A082666 * A082668 A082669 A082670

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 18 2003

Status

approved