A213489 Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w + x + y.

1, 7, 19, 37, 64, 103, 154, 217, 295, 391, 505, 637, 790, 967, 1168, 1393, 1645, 1927, 2239, 2581, 2956, 3367, 3814, 4297, 4819, 5383, 5989, 6637, 7330, 8071, 8860, 9697, 10585, 11527, 12523, 13573, 14680, 15847, 17074, 18361, 19711, 21127

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 (4,-7,8,-7,4,-1).

Crossrefs

Cf. A212959, A213488.

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]]   (* A213489 *)

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.: (1 + 3*x - 2*x^2 + 2* x^3 - x^5)/((1 - x)^4 (1 + x^2)). [corrected by Georg Fischer, May 10 2019]

a(n) + A213488(n) = (n+1)^3.