A212690 Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|<=n+|y-z|.

0, 1, 16, 75, 236, 567, 1172, 2157, 3672, 5861, 8920, 13031, 18436, 25355, 34076, 44857, 58032, 73897, 92832, 115171, 141340, 171711, 206756, 246885, 292616, 344397, 402792, 468287, 541492, 622931, 713260, 813041, 922976, 1043665

Offset: 0

Author

Clark Kimberling, May 25 2012

Keywords

• nonn
• easy

Comments

a(n)+A212689(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]]   (* A212690 *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 16, 75, 236, 567, 1172}, 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 + 13*x^2 + 28*x^3 + 32*x^4 + 9*x^5 + x^6)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).