A213399 Number of (w,x,y) with all terms in {0,...,n} and max(|w-x|,|x-y|) = x.

1, 4, 14, 23, 43, 58, 88, 109, 149, 176, 226, 259, 319, 358, 428, 473, 553, 604, 694, 751, 851, 914, 1024, 1093, 1213, 1288, 1418, 1499, 1639, 1726, 1876, 1969, 2129, 2228, 2398, 2503, 2683, 2794, 2984, 3101, 3301, 3424, 3634, 3763, 3983, 4118

Offset: 0

Author

Clark Kimberling, Jun 13 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A212959.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A212959.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[x == Max[Abs[w - x], Abs[x - y]], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]]   (* A213399 *)

PARI

Vec((1+3*x+8*x^2+3*x^3+x^4) / ((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016

Formula

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

G.f.: (1 + 3*x + 8*x^2 + 3*x^3 + x^4)/((1 - x)^3 * (1 + x)^2).

From Colin Barker, Jan 26 2016: (Start)

a(n) = (8*n^2+2*(-1)^n*n+8*n+(-1)^n+3)/4.

a(n) = (4*n^2+5*n+2)/2 for n even.

a(n) = (4*n^2+3*n+1)/2 for n odd.

(End)