OFFSET
0,3
COMMENTS
Every term is even. For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, -1).
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2012
STATUS
approved