A213480 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| != w+x+y.

0, 4, 16, 46, 95, 175, 285, 439, 634, 886, 1190, 1564, 2001, 2521, 3115, 3805, 4580, 5464, 6444, 7546, 8755, 10099, 11561, 13171, 14910, 16810, 18850, 21064, 23429, 25981, 28695, 31609, 34696, 37996, 41480, 45190, 49095, 53239, 57589

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.

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]]   (* A213480 *)

Formula

a(n) + A213479(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.: (4*x + 8*x^2 + 10*x^3 + 3*x^4 - x^5)/((1 - x)^4*(1 + x)^2).

a(n) = (8*n^3 + 15*n^2 + 4*n + 5 - (2*n+5)*((n+1) mod 2))/8. - Ayoub Saber Rguez, Nov 20 2021