cp's OEIS Frontend

A212976 Number of (w,x,y) with all terms in {0,...,n} and odd range.

%I A212976 #24 Jan 21 2017 10:03:55
%S A212976 0,6,12,36,60,114,168,264,360,510,660,876,1092,1386,1680,2064,2448,
%T A212976 2934,3420,4020,4620,5346,6072,6936,7800,8814,9828,11004,12180,13530,
%U A212976 14880,16416,17952,19686,21420,23364,25308,27474,29640,32040
%N A212976 Number of (w,x,y) with all terms in {0,...,n} and odd range.
%C A212976 a(n) + A212975(n) = (n+1)^3. Six divides every term.
%C A212976 For a guide to related sequences, see A212959.
%H A212976 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A212976 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A212976 G.f.: f(x)/g(x), where f(x) = 6*x*(1 + x^2) and g(x) = ((1-x)^4)*(1+x)^2.
%F A212976 a(n+1) = 6*A005993(n). [_Bruno Berselli_, Jun 15 2012]
%t A212976 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212976 (Do[If[Mod[Max[w, x, y] - Min[w, x, y], 2] == 1,
%t A212976    s = s + 1],
%t A212976 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212976 m = Map[t[#] &, Range[0, 60]]   (* A212976 *)
%t A212976 m/6  (* A005993 except for initial 0 *)
%t A212976 LinearRecurrence[{2,1,-4,1,2,-1},{0,6,12,36,60,114},40] (* _Harvey P. Dale_, Jan 21 2017 *)
%Y A212976 Cf. A005993, A212959, A212975.
%K A212976 nonn,easy
%O A212976 0,2
%A A212976 _Clark Kimberling_, Jun 03 2012