A212682 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|>=|y-z|.

0, 1, 12, 57, 168, 395, 792, 1435, 2400, 3789, 5700, 8261, 11592, 15847, 21168, 27735, 35712, 45305, 56700, 70129, 85800, 103971, 124872, 148787, 175968, 206725, 241332, 280125, 323400, 371519, 424800, 483631, 548352, 619377, 697068

Offset: 0

Author

Clark Kimberling, May 24 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[x - y] >= Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212682 *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 12, 57, 168, 395, 792}, 40]

Formula

a(n)=3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).

G.f.: (x + 9*x^2 + 22*x^3 + 14*x^4 + 3*x^5 - x^6)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).