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%I #12 Jun 13 2015 00:54:14
%S 0,4,18,64,150,324,588,1024,1620,2500,3630,5184,7098,9604,12600,16384,
%T 20808,26244,32490,40000,48510,58564,69828,82944,97500,114244,132678,
%U 153664,176610,202500,230640,262144,296208,334084,374850
%N Number of (w,x,y,z) with all terms in {0,...,n}, w even and x odd.
%C Every term is even.
%C For a guide to related sequences, see A211795.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).
%F a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).
%F G.f.: -2*x*(2+5*x+10*x^2+5*x^3+2*x^4) / ( (1+x)^3*(x-1)^5 ).
%F a(n) = (2n(n+2)-(-1)^n+1)(n+1)^2/8. [_Bruno Berselli_, Jun 11 2012]
%t t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 1), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t Map[t[#] &, Range[0, 40]] (* A212766 *)
%t %/2 (* integers *)
%t LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 4, 18, 64, 150, 324, 588, 1024}, 40]
%Y Cf. A211795.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, May 29 2012
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