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A212257 Number of (v,w,x,y,z) with all terms in {0,1,...,n} and v=average(w,x,y,z).

%I A212257 #11 Sep 10 2016 12:28:16
%S A212257 1,2,21,64,157,322,601,1024,1641,2498,3661,5184,7141,9602,12657,16384,
%T A212257 20881,26242,32581,40000,48621,58562,69961,82944,97657,114242,132861,
%U A212257 153664,176821,202498,230881,262144,296481,334082,375157
%N A212257 Number of (v,w,x,y,z) with all terms in {0,1,...,n} and v=average(w,x,y,z).
%C A212257 For a guide to related sequences, see A211795.
%H A212257 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,0,-4,6,-4,1)
%F A212257 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-4*a(n-5)+6*a(n-6)-4*a(n-7)+a(n-8).
%F A212257 From _Benedict W. J. Irwin_, Sep 05 2016: (Start)
%F A212257 a(n) = (1+7*(-1)^n)/8+n+3*n^2/2+n^3+n^4/4-sin(n*Pi/2).
%F A212257 G.f.: 7/(8*(1+x))-x/(1+x^2)+(-1-26*x-16*x^2-6*x^3+x^4)/(8*(x-1)^5).
%F A212257 (End)
%t A212257 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212257 (Do[If[4 v == w + x + y + z, s = s + 1], {v, 0, #},
%t A212257 {w, 0, #}, {x, 0, #}, {y, 0, #}, {z, 0, #}] &[n]; s)]];
%t A212257 Map[t[#] &, Range[0, 40]]   (* A212257 *)
%t A212257 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A212257 Table[(1+7(-1)^n)/8+n+3n^2/2+n^3+n^4/4-Sin[n Pi/2], {n, 0, 30}] (* _Benedict W. J. Irwin_, Sep 05 2016 *)
%Y A212257 Cf. A211795.
%K A212257 nonn
%O A212257 0,2
%A A212257 _Clark Kimberling_, May 15 2012