A213389 Number of (w,x,y) with all terms in {0,...,n} and max(w,x,y) < 2*min(w,x,y).

0, 1, 2, 9, 16, 35, 54, 91, 128, 189, 250, 341, 432, 559, 686, 855, 1024, 1241, 1458, 1729, 2000, 2331, 2662, 3059, 3456, 3925, 4394, 4941, 5488, 6119, 6750, 7471, 8192, 9009, 9826, 10745, 11664, 12691, 13718, 14859, 16000, 17261, 18522

Offset: 0

Author

Clark Kimberling, Jun 11 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Max[w, x, y] < 2*Min[w, x, y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 50]]   (* A213389 *)
LinearRecurrence[{2,1,-4,1,2,-1},{0,1,2,9,16,35},50] (* Harvey P. Dale, Jun 24 2025 *)

PARI

a(n)=n*ceil(n^2/4) \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = (n+1)^3 - A213390(n).

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

G.f.: (x + 4*x^3 + x^5)/((1 - x)^4*(1 + x)^2).

a(n) = n * ceiling(n^2/4). - Wesley Ivan Hurt, Jun 15 2013

a(n) = n*(2*n^2+3*(1-(-1)^n))/8. - Luce ETIENNE, Jul 17 2016