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A212763 Number of (w,x,y,z) with all terms in {0,...,n}, and w, x and y odd.

%I A212763 #19 Oct 01 2015 06:56:48
%S A212763 0,2,3,32,40,162,189,512,576,1250,1375,2592,2808,4802,5145,8192,8704,
%T A212763 13122,13851,20000,21000,29282,30613,41472,43200,57122,59319,76832,
%U A212763 79576,101250,104625,131072,135168,167042,171955,209952,215784
%N A212763 Number of (w,x,y,z) with all terms in {0,...,n}, and w, x and y odd.
%C A212763 For a guide to related sequences, see A211795.
%H A212763 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).
%F A212763 a(n) = a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9).
%F A212763 G.f.: x*(2+x+21*x^2+4*x^3+18*x^4+x^5+x^6) / ( (1+x)^4*(1-x)^5 ).
%F A212763 a(n) = (n+1)*(2*n^3+3*n^2+3*n+1-(3*n^2+3*n+1)*(-1)^n)/16. - _Luce ETIENNE_, Oct 01 2015
%F A212763 a(n) = A212759(-n-2). [_Bruno Berselli_, Oct 01 2015]
%t A212763 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 1) && (Mod[x, 2] == 1) && (Mod[y, 2] == 1), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212763 Map[t[#] &, Range[0, 50]]  (* A212763 *)
%t A212763 LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 2, 3, 32, 40,162, 189, 512, 576}, 45]
%o A212763 (PARI) a(n) = (n+1)*(2*n^3+3*n^2+3*n+1-(3*n^2+3*n+1)*(-1)^n)/16;
%o A212763 vector(100, n, a(n-1)) \\ _Altug Alkan_, Oct 01 2015
%Y A212763 Cf. A211795, A212759.
%K A212763 nonn,easy
%O A212763 0,2
%A A212763 _Clark Kimberling_, May 29 2012