A212688 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|>=n+|y-z|.

0, 0, 4, 14, 44, 98, 200, 356, 600, 940, 1420, 2050, 2884, 3934, 5264, 6888, 8880, 11256, 14100, 17430, 21340, 25850, 31064, 37004, 43784, 51428, 60060, 69706, 80500, 92470, 105760, 120400, 136544, 154224, 173604, 194718, 217740

Offset: 0

Author

Clark Kimberling, May 25 2012

Keywords

• nonn
• easy

Comments

a(n)+A212687(n)=n^4.

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[2 Abs[w - x] >= n + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212688 *)
%/2  (* integers *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 0, 4, 14, 44, 98, 200}, 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.: (4*x^2 + 2*x^3 + 6*x^4)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).