A212689 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|>n+|y-z|.

0, 0, 0, 6, 20, 58, 124, 244, 424, 700, 1080, 1610, 2300, 3206, 4340, 5768, 7504, 9624, 12144, 15150, 18660, 22770, 27500, 32956, 39160, 46228, 54184, 63154, 73164, 84350, 96740, 110480, 125600, 142256, 160480, 180438, 202164, 225834

Offset: 0

Author

Clark Kimberling, May 25 2012

Keywords

• nonn
• easy

Comments

a(n)+A212690(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, A212690.

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]]   (* A212689 *)
%/2 (* integers *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 0, 0, 6, 20, 58, 124}, 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.: (6*x^3 + 2*x^4 + 4*x^5)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).