OFFSET
0,2
COMMENTS
The gap sizes are |w-x|, |x-y|, |y-z|. For a guide to related sequences, see A211795.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 31 2012
STATUS
approved