OFFSET
0,3
COMMENTS
Also, the number of (w,x,y,z) with all terms in {1,...,n} and |x-y|>|y-z|.
Every term is even.
For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).
FORMULA
a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).
G.f.: (4*x^2 + 12*x^3 + 20*x^4 + 10*x^5 + 2*x^6)/(1 - 3*x + x^2 + 5*x^3 - 5*x^4 - x^5 + 3*x^6 - x^7).
a(n) + A212682(n) = n^4.
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[x - y] < Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212681 *)
%/2 (* integers *)
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 0, 4, 24, 88, 230, 504}, 40]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2012
STATUS
approved