A213498 Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|,|x-y|,|y-w|).

0, 4, 15, 43, 88, 164, 267, 415, 600, 844, 1135, 1499, 1920, 2428, 3003, 3679, 4432, 5300, 6255, 7339, 8520, 9844, 11275, 12863, 14568, 16444, 18447, 20635, 22960, 25484, 28155, 31039, 34080, 37348, 40783, 44459, 48312, 52420, 56715

Offset: 0

Author

Clark Kimberling, Jun 14 2012

Keywords

• nonn
• easy

Comments

a(n)+A212965 = (n+1)^3.

For a guide to related sequences, see A212959.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• 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[Abs[w - x], Abs[x - y], Abs[y - w]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]   (* A213498 *)
LinearRecurrence[{2,1,-4,1,2,-1},{0,4,15,43,88,164},50] (* Harvey P. Dale, Mar 27 2020 *)

Formula

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 + 7*x^2 + 9*x^3 + 3*x^4 + x^5)/((-1 + x)^4*(1 + x)^2).

a(n) = (2*n*(4*n^2+5*n+5) - (2*n+1)*(-1)^n + 1)/8.