A213045 Number of (w,x,y) with all terms in {0,...,n} and 2*|w-x| > max(w,x,y) - min(w,x,y).

0, 4, 14, 36, 72, 128, 206, 312, 448, 620, 830, 1084, 1384, 1736, 2142, 2608, 3136, 3732, 4398, 5140, 5960, 6864, 7854, 8936, 10112, 11388, 12766, 14252, 15848, 17560, 19390, 21344, 23424, 25636, 27982, 30468, 33096, 35872, 38798, 41880

Offset: 0

Author

Clark Kimberling, Jun 10 2012

Keywords

• nonn
• easy

Comments

Every term is even.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

See A212959 for a guide to related sequences.

Cf. A087035, A212685.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[Max[w, x, y] - Min[w, x, y] < 2 Abs[w - x], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 45]]   (* this sequence *)
m/2  (* integers *)
LinearRecurrence[{3,-2,-2,3,-1},{0,4,14,36,72},50] (* Harvey P. Dale, Jul 31 2013 *)

Formula

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

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

a(n) = (n+1)^3 - A087035(n+1).

a(n) = 2*A212685(n+1) = (2*n*(4*n^2+9*n+8) - 3*(-1)^n + 3)/12. [Bruno Berselli, Jun 11 2012]