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

0,2

Comments

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

Links

Table of n, a(n) for n=0..44.

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

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.

Example

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).

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 *)

Crossrefs

Cf. A211795, A212900.

Sequence in context: A024834 A143867 A024809 * A049729 A189581 A206804

Adjacent sequences: A212898 A212899 A212900 * A212902 A212903 A212904

Keyword

nonn,easy

Author

Clark Kimberling, May 31 2012

Status

approved