A213502 Number of (w,x,y) with all terms in {0,...,n} and x != min(|w-x|, |x-y|).

0, 4, 17, 47, 98, 178, 291, 445, 644, 896, 1205, 1579, 2022, 2542, 3143, 3833, 4616, 5500, 6489, 7591, 8810, 10154, 11627, 13237, 14988, 16888, 18941, 21155, 23534, 26086, 28815, 31729, 34832, 38132, 41633, 45343, 49266, 53410, 57779

Offset: 0

Author

Clark Kimberling, Jun 14 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

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

Crossrefs

Cf. A212959, A213398.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[x != Min[Abs[w - x], Abs[x - y]], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]]

Formula

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

G.f.: x*(4 + 5*x + 4*x^2 - x^3)/((1 - x)^4*(1 + x)).

a(n) = (n+1)^3 - A213398(n).

a(n) = (2*n*(2*n^2+4*n+1) - (-1)^n + 1)/4. - Bruno Berselli, Jul 02 2012