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
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
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 18 2003
STATUS
approved