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A212759 Number of (w,x,y,z) with all terms in {0,...,n} and w, x, and y even.

%I A212759 #15 Sep 23 2015 09:43:16
%S A212759 1,2,24,32,135,162,448,512,1125,1250,2376,2592,4459,4802,7680,8192,
%T A212759 12393,13122,19000,20000,27951,29282,39744,41472,54925,57122,74088,
%U A212759 76832,97875,101250,126976,131072,162129,167042,204120,209952
%N A212759 Number of (w,x,y,z) with all terms in {0,...,n} and w, x, and y even.
%C A212759 For a guide to related sequences, see A211795.
%H A212759 <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 A212759 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 A212759 G.f.: (1+x+18*x^2+21*x^4+x^5+2*x^6+4*x^3 ) / ( (1+x)^4*(1-x)^5 ).
%F A212759 a(n) = (n+1)*(2*n^3+9*n^2+15*n+9+(3*n^2+9*n+7)*(-1)^n)/16. - _Luce ETIENNE_, Sep 23 2015
%t A212759 t = Compile[{{n, _Integer}},
%t A212759 Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 0) && (Mod[y, 2] == 0),
%t A212759 s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212759 Map[t[#] &, Range[0, 50]]  (* A212759 *)
%t A212759 LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {1, 2, 24, 32, 135, 162, 448, 512, 1125}, 45]
%Y A212759 Cf. A211795.
%K A212759 nonn,easy
%O A212759 0,2
%A A212759 _Clark Kimberling_, May 29 2012