OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: (1 + 3*x + 5*x^2 + x^3 - x^4)/((1 - x)^3 * (1 + x)^2).
From Colin Barker, Jan 27 2016: (Start)
a(n) = (18*n^2+2*(-1)^n*n+42*n+5*(-1)^n+11)/16.
a(n) = (9*n^2+22*n+8)/8 for n even.
a(n) = (9*n^2+20*n+3)/8 for n odd. (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]] (* A213479 *)
PROG
(PARI) Vec((1+3*x+5*x^2+x^3-x^4)/((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 13 2012
STATUS
approved