A212968 Number of (w,x,y) with all terms in {0,...,n} and w>=range{w,x,y}.

1, 5, 17, 38, 75, 127, 203, 300, 429, 585, 781, 1010, 1287, 1603, 1975, 2392, 2873, 3405, 4009, 4670, 5411, 6215, 7107, 8068, 9125, 10257, 11493, 12810, 14239, 15755, 17391, 19120, 20977, 22933, 25025, 27222, 29563, 32015, 34619, 37340

Offset: 0

Author

Clark Kimberling, Jun 02 2012

Keywords

• nonn
• easy

Comments

a(n)+A212967(n) = (n+1)^3.

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[w >= (Max[w, x, y] - Min[w, x, y]), s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]]   (* A212968 *)

Formula

a(n) = (n+1)*(14*n*(n+2)+3*(-1)^n+21)/24.

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.: f(x)/g(x), where f(x) = 1 + 3*x + 6*x^2 + 3*x^3 + x^4 and g(x) = ((1-x)^4)(1+x)^2.