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A212761 Number of (w,x,y,z) with all terms in {0,...,n}, w odd, x and y even.

%I A212761 #15 Oct 09 2015 04:53:19
%S A212761 0,2,12,32,90,162,336,512,900,1250,1980,2592,3822,4802,6720,8192,
%T A212761 11016,13122,17100,20000,25410,29282,36432,41472,50700,57122,68796,
%U A212761 76832,91350,101250,119040,131072,152592,167042,192780,209952,240426
%N A212761 Number of (w,x,y,z) with all terms in {0,...,n}, w odd, x and y even.
%C A212761 Every term is even.
%C A212761 For a guide to related sequences, see A211795.
%H A212761 <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 A212761 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 A212761 G.f.: 2*x*(1+5*x+6*x^2+9*x^3+2*x^4+x^5) / ( (1+x)^4*(1-x)^5 ).
%F A212761 a(n) = (n+1)*(2*n^3+7*n^2+7*n+1+(n^2+n-1)*(-1)^n)/16. - _Luce ETIENNE_, Oct 10 2015
%t A212761 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 1) && (Mod[x, 2] == 0) && (Mod[y, 2] == 0), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212761 Map[t[#] &, Range[0, 50]]  (* A212761 *)
%t A212761 %/2 (* integers *)
%t A212761 LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 2, 12, 32, 90, 162, 336, 512, 900}, 45]
%Y A212761 Cf. A211795.
%K A212761 nonn,easy
%O A212761 0,2
%A A212761 _Clark Kimberling_, May 29 2012