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A212762 Number of (w,x,y,z) with all terms in {0,...,n}, w and x odd, y even.

%I A212762 #17 Sep 19 2015 06:13:32
%S A212762 0,2,6,32,60,162,252,512,720,1250,1650,2592,3276,4802,5880,8192,9792,
%T A212762 13122,15390,20000,23100,29282,33396,41472,46800,57122,63882,76832,
%U A212762 85260,101250,111600,131072,143616,167042,182070,209952,227772
%N A212762 Number of (w,x,y,z) with all terms in {0,...,n}, w and x odd, y even.
%C A212762 Every term is even.
%C A212762 For a guide to related sequences, see A211795.
%H A212762 <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 A212762 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 A212762 G.f.: 2*x*(1+2*x+9*x^2+6*x^3+5*x^4+x^5) / ( (1+x)^4*(1-x)^5 ).
%F A212762 a(n) = (n+1)*(2*n^3+5*n^2+3*n+1-(n^2+3*n+1)*(-1)^n)/16. - _Luce ETIENNE_, Sep 19 2015
%t A212762 t = Compile[{{n, _Integer}},  Module[{s = 0}, (Do[If[(Mod[w, 2] == 1) && (Mod[x, 2] == 1) && (Mod[y, 2] == 0), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212762 Map[t[#] &, Range[0, 50]]  (* A212762 *)
%t A212762 %/2 (* integers *)
%t A212762 LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 2, 6, 32, 60, 162, 252, 512, 720}, 45]
%Y A212762 Cf. A211795.
%K A212762 nonn
%O A212762 0,2
%A A212762 _Clark Kimberling_, May 29 2012