OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
FORMULA
a(n) + A006918(n) = (n+1)^3.
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.: (1 + 5*x + 10*x^2 + 6*x^3 + x^4)/((1 - x)^4 (1 + x)^2)).
From Ayoub Saber Rguez, Dec 29 2021: (Start)
a(n) = (23*n^3 + 66*n^2 + 64*n + 24 - (3*n+6)*(n mod 2))/24. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x + y >= Abs[w - x] + Abs[x - y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]] (* A213481 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 13 2012
STATUS
approved