A212755 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|=max{w,x,y,z}-min{w,x,y,z}.

1, 10, 37, 96, 205, 386, 665, 1072, 1641, 2410, 3421, 4720, 6357, 8386, 10865, 13856, 17425, 21642, 26581, 32320, 38941, 46530, 55177, 64976, 76025, 88426, 102285, 117712, 134821, 153730, 174561, 197440, 222497, 249866, 279685

Offset: 0

Author

Clark Kimberling, May 28 2012

Keywords

• nonn
• easy
• changed

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] == Max[w, x, y, z] - 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]]   (* A212755 *)

Formula

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).

G.f.: (-1-5*x+3*x^2-x^3)/(x-1)^5.

E.g.f.: exp(x)*(6 + 54*x + 54*x^2 + 14*x^3 + x^4)/6. - Stefano Spezia, Aug 28 2025