A212901 Number of (w,x,y,z) with all terms in {0,...,n} and equal consecutive gap sizes.

1, 4, 13, 26, 45, 66, 95, 126, 163, 204, 251, 300, 357, 416, 481, 550, 625, 702, 787, 874, 967, 1064, 1167, 1272, 1385, 1500, 1621, 1746, 1877, 2010, 2151, 2294, 2443, 2596, 2755, 2916, 3085, 3256, 3433, 3614, 3801, 3990, 4187, 4386, 4591

Offset: 0

Author

Clark Kimberling, May 31 2012

Keywords

• nonn
• easy

Comments

The gap sizes are |w-x|, |x-y|, |y-z|. For a guide to related sequences, see A211795.

Examples

			a(1)=4 counts these (w,x,y,z): (0,0,0,0), (1,1,1,1), (0,1,0,1), (1,0,1,0).
		

Links

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

Crossrefs

Cf. A211795, A212900.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] == Abs[x - y] == Abs[y - z], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 40]]   (* A212901 *)

Formula

a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6).

G.f.: f(x)/g(x), where f(x) = 1 + 3*x + 8*x^2 + 9*x^3 + 7*x^4 and g(x) = (1 + 2*x + 2*x^2 + x^3)(1 - x)^3.