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A212765 Number of (w,x,y,z) with all terms in {0,...,n}, w even and x, y, and z odd.

%I A212765 #15 Jun 13 2015 00:54:14
%S A212765 0,1,2,16,24,81,108,256,320,625,750,1296,1512,2401,2744,4096,4608,
%T A212765 6561,7290,10000,11000,14641,15972,20736,22464,28561,30758,38416,
%U A212765 41160,50625,54000,65536,69632,83521,88434,104976,110808,130321,137180
%N A212765 Number of (w,x,y,z) with all terms in {0,...,n}, w even and x, y, and z odd.
%C A212765 For a guide to related sequences, see A211795.
%H A212765 <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 A212765 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 A212765 G.f.: x*(1+x+10*x^2+7*x^4+x^5+4*x^3) / ( (1+x)^4*(1-x)^5 ).
%F A212765 a(n)=((2*n^4+6*n^3+6*n^2+4*n+1)-(2*n^3+6*n^2+4*n+1)*(-1)^n)/32. - _Luce ETIENNE_, Apr 05 2014
%t A212765 t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 1) && (Mod[y, 2] == 1) && (Mod[z, 2] == 1), s++], {w, 0, n}, {x, 0, n},
%t A212765 {y, 0, n}, {z, 0, n}]; s)]];
%t A212765 Map[t[#] &, Range[0, 40]]  (* A212765 *)
%t A212765 LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {0, 1, 2, 16, 24, 81, 108, 256, 320}, 40]
%Y A212765 Cf. A211795.
%K A212765 nonn,easy
%O A212765 0,3
%A A212765 _Clark Kimberling_, May 29 2012