OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).
FORMULA
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5).
G.f.: (1 + x - x^2 + x^3 + x^4)/((1 - x)^3 (1 + x^2)).
From Ayoub Saber Rguez, Dec 31 2021: (Start)
a(n) + A213485(n) = (n+1)^3.
a(n) = 3*A054925(n+1) + 1.
a(n) = 3*(A192447(n+1)/2) + 1.
a(n) = (3*n^2 + 3*n + 4 + 3*((n+1) mod 4 - (n+1) mod 2))/4. (End)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x + y == Abs[w - x] + Abs[x - y] + Abs[y - w],
s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
Map[t[#] &, Range[0, 60]] (* A213484 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 13 2012
STATUS
approved