A213486 Number of (w,x,y) with all terms in {0,...,n} and |w-x|+|x-y|+|y-w| > w+x+y.

0, 3, 12, 27, 48, 78, 120, 174, 240, 321, 420, 537, 672, 828, 1008, 1212, 1440, 1695, 1980, 2295, 2640, 3018, 3432, 3882, 4368, 4893, 5460, 6069, 6720, 7416, 8160, 8952, 9792, 10683, 11628, 12627, 13680, 14790, 15960, 17190, 18480, 19833

Offset: 0

Author

Clark Kimberling, Jun 13 2012

Keywords

• nonn
• easy

Comments

Every term is divisible by 3.

For a guide to related sequences, see A212959.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-7,4,-1).

Crossrefs

Cf. A212959, A213487.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w + x + y < 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]]   (* A213486 *)

Formula

a(n) = 4*a(n-1)-7*a(n-2)+8*a(n-3)-7*a(n-4)+4*a(n-5)-a(n-6).

G.f.: 3*x/((1 - x)^4 (1 + x^2)).

a(n) = (n+1)^3 - A213487(n).