A212692 Number of (w,x,y,z) with all terms in {1,...,n} and w<|x-y|+|y-z|.

0, 0, 6, 22, 54, 106, 184, 292, 436, 620, 850, 1130, 1466, 1862, 2324, 2856, 3464, 4152, 4926, 5790, 6750, 7810, 8976, 10252, 11644, 13156, 14794, 16562, 18466, 20510, 22700, 25040, 27536, 30192, 33014, 36006, 39174, 42522, 46056, 49780

Offset: 0

Author

Clark Kimberling, May 23 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

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

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == Abs[x - y] + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212692 *)
%/2  (* integers *)
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 6, 22, 54}, 40]

Formula

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

G.f.: (6*x^2 + 4*x^3)/(1 - 3*x + 2* x^2 + 2*x^3 - 3*x^4 + x^5).