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) + A213483(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.: (3*x + 8*x^2 + 10*x^3 + 3*x^4 - x^5)/((1 - x)^4*(1 + x)^2).
From Ayoub Saber Rguez, Dec 29 2021: (Start)
a(n) = (23*n^3 + 39*n^2 + n + 9 - (3*n+9)*((n+1) 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]] (* A213482 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Jun 13 2012
STATUS
approved