A213489 - OEIS

%I #13 May 10 2019 18:38:55

%S 1,7,19,37,64,103,154,217,295,391,505,637,790,967,1168,1393,1645,1927,

%T 2239,2581,2956,3367,3814,4297,4819,5383,5989,6637,7330,8071,8860,

%U 9697,10585,11527,12523,13573,14680,15847,17074,18361,19711,21127

%N Number of (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| + |y-w| >= w + x + y.

%C For a guide to related sequences, see A212959.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,8,-7,4,-1).

%F a(n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 7*a(n-4) + 4*a(n-5) - a(n-6).

%F G.f.: (1 + 3*x - 2*x^2 + 2* x^3 - x^5)/((1 - x)^4 (1 + x^2)). [corrected by _Georg Fischer_, May 10 2019]

%F a(n) + A213488(n) = (n+1)^3.

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[w + x + y <= Abs[w - x] + Abs[x - y] + Abs[y - w],

%t s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

%t m = Map[t[#] &, Range[0, 60]]   (* A213489 *)

%Y Cf. A212959, A213488.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 13 2012