A212568 Number of (w,x,y,z) with all terms in {1,...,n} and w<|x-y|+|y-z|.

0, 0, 2, 24, 98, 272, 608, 1184, 2092, 3440, 5350, 7960, 11422, 15904, 21588, 28672, 37368, 47904, 60522, 75480, 93050, 113520, 137192, 164384, 195428, 230672, 270478, 315224, 365302, 421120, 483100, 551680, 627312, 710464, 801618

Offset: 0

Author

Clark Kimberling, May 23 2012

Keywords

• nonn
• easy

Comments

a(n) + A212675(n) = n^4.

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -5, 0, 5, -4, 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]]   (* A212568 *)
%/2 (* integers *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 0, 2, 24, 98, 272}, 20]

Formula

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

G.f.: (2*x^2+16*x^3+12*x^4)/(1-4*x+5*x^2-5*x^4+4*x^5-x^6). [corrected by Georg Fischer, May 03 2019]