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A212680
Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|=|y-z|+1.
2
0, 0, 4, 18, 56, 120, 228, 378, 592, 864, 1220, 1650, 2184, 2808, 3556, 4410, 5408, 6528, 7812, 9234, 10840, 12600, 14564, 16698, 19056, 21600, 24388, 27378, 30632, 34104, 37860, 41850, 46144, 50688, 55556, 60690, 66168, 71928, 78052
OFFSET
0,3
COMMENTS
Every term is even. For a guide to related sequences, see A211795.
FORMULA
a(n)=2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
G.f.: (2 x^2 (2 + x) (1 + 2 x + 3 x^2))/((-1 + x)^4 (1 + x)^2). [corrected by Clark Kimberling, Feb 27 2018]
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[x - y] == Abs[y - z] + 1, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212680 *)
%/2 (* integers *)
LinearRecurrence[{2, 1, -4, 1, 2, -1 }, {0, 0, 4, 18, 56, 120 }, 40]
CROSSREFS
Cf. A211795.
Sequence in context: A242206 A181411 A238915 * A027286 A119044 A058851
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2012
STATUS
approved