%I #24 Jan 21 2017 10:03:55

%S 0,6,12,36,60,114,168,264,360,510,660,876,1092,1386,1680,2064,2448,

%T 2934,3420,4020,4620,5346,6072,6936,7800,8814,9828,11004,12180,13530,

%U 14880,16416,17952,19686,21420,23364,25308,27474,29640,32040

%N Number of (w,x,y) with all terms in {0,...,n} and odd range.

%C a(n) + A212975(n) = (n+1)^3. Six divides every term.

%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 (2,1,-4,1,2,-1).

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

%F G.f.: f(x)/g(x), where f(x) = 6*x*(1 + x^2) and g(x) = ((1-x)^4)*(1+x)^2.

%F a(n+1) = 6*A005993(n). [_Bruno Berselli_, Jun 15 2012]

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

%t (Do[If[Mod[Max[w, x, y] - Min[w, x, y], 2] == 1,

%t s = s + 1],

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

%t m = Map[t[#] &, Range[0, 60]] (* A212976 *)

%t m/6 (* A005993 except for initial 0 *)

%t LinearRecurrence[{2,1,-4,1,2,-1},{0,6,12,36,60,114},40] (* _Harvey P. Dale_, Jan 21 2017 *)

%Y Cf. A005993, A212959, A212975.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 03 2012