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A212901
Number of (w,x,y,z) with all terms in {0,...,n} and equal consecutive gap sizes.
2
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.
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
Sequence in context: A024834 A143867 A024809 * A049729 A189581 A206804
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 31 2012
STATUS
approved