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A212764 Number of (w,x,y,z) with all terms in {0,...,n}, w, x and y odd, and z odd.

%I A212764 #17 Jun 13 2015 00:54:14
%S A212764 0,1,8,16,54,81,192,256,500,625,1080,1296,2058,2401,3584,4096,5832,
%T A212764 6561,9000,10000,13310,14641,19008,20736,26364,28561,35672,38416,
%U A212764 47250,50625,61440,65536,78608,83521,99144,104976,123462,130321
%N A212764 Number of (w,x,y,z) with all terms in {0,...,n}, w, x and y odd, and z odd.
%C A212764 For a guide to related sequences, see A211795.
%H A212764 <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 A212764 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 A212764 G.f.: x*(1+7*x+4*x^2+10*x^3+x^4+x^5) / ( (1+x)^4*(1-x)^5 ).
%F A212764 a(n) = (2*n^4+10*n^3+18*n^2+12*n+1+(2*n^3+6*n^2+4*n-1)*(-1)^n)/32. - _Luce ETIENNE_, May 12 2015
%t A212764 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2]== 0) && (Mod[y, 2] == 0) && (Mod[z, 2] == 1), s++], {w, 0, n}, {x, 0, n},
%t A212764 {y, 0, n}, {z, 0, n}]; s)]];
%t A212764 Map[t[#] &, Range[0, 40]]  (* A212764 *)
%t A212764 LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 1, 8, 16, 54, 81, 192, 256, 500}, 45]
%Y A212764 Cf. A211795.
%K A212764 nonn,easy
%O A212764 0,3
%A A212764 _Clark Kimberling_, May 29 2012