OFFSET
0,2
COMMENTS
For a guide to related sequences, see A212959.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(n) = (14*n*(n+1) + (2*n+1)*(-1)^n + 7)/8.
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: (1 + 3*x + 6*x^2 + 3*x^3 + x^4)/((1 + x)^2*(1 - x)^3).
From Ayoub Saber Rguez, Dec 06 2021: (Start)
a(n) + A213498(n) = (n+1)^3.
a(n) = (7*n^2 + 8*n + 4 - (2*n+1)*(n mod 2))/4. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w == Max[w, x, y] - Min[w, x, y], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 50]] (* A212965 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 02 2012
STATUS
approved