A213482 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| > w+x+y.

0, 3, 14, 41, 87, 161, 265, 409, 594, 831, 1120, 1473, 1889, 2381, 2947, 3601, 4340, 5179, 6114, 7161, 8315, 9593, 10989, 12521, 14182, 15991, 17940, 20049, 22309, 24741, 27335, 30113, 33064, 36211, 39542, 43081, 46815, 50769, 54929

Offset: 0

Author

Clark Kimberling, Jun 13 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, A213479, A213481, A213483.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x + y > Abs[w - x] + Abs[x - y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]]   (* A213482 *)

Formula

a(n) + A213483(n) = (n+1)^3.

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.: (3*x + 8*x^2 + 10*x^3 + 3*x^4 - x^5)/((1 - x)^4*(1 + x)^2).

From Ayoub Saber Rguez, Dec 29 2021: (Start)

a(n) = A213481(n) - A213479(n).

a(n) = (23*n^3 + 39*n^2 + n + 9 - (3*n+9)*((n+1) mod 2))/24. (End)