A212745 Number of (w,x,y,z) with all terms in {0,...,n} and w=max{w,x,y,z}-2*min{w,x,y,z}.

1, 8, 27, 83, 162, 277, 495, 730, 1025, 1513, 1988, 2547, 3413, 4212, 5119, 6471, 7678, 9017, 10963, 12662, 14517, 17165, 19440, 21895, 25353, 28288, 31427, 35803, 39482, 43389, 48791, 53298, 58057, 64593, 70012, 75707, 83485, 89900

Offset: 0

Author

Clark Kimberling, May 26 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == Max[w, x, y, z] - 2 Min[w, x, y, z],
  s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]]   (* A212745  *)
LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {1, 8, 27, 83, 162, 277, 495, 730, 1025, 1513}, 40]

Formula

a(n)=a(n-1)+3*a(n-3)-3*a(n-4)-3*a(n-6)+3*a(n-7)+a(n-9)-a(n-10).

G.f.: (1+x)*(x^8+6*x^7+13*x^6+40*x^5+18*x^4+40*x^3+13*x^2+6*x+1) / ( (1+x+x^2)^3*(1-x)^4 ).