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A212242 Number of (u,v,w,x,y,z) with all terms in {0,1,...,n} and 5u=v+w+x+y+z.

%I A212242 #14 Jan 05 2025 05:50:39
%S A212242 1,2,53,204,625,1556,3357,6558,11809,20000,32211,49762,74263,107564,
%T A212242 151875,209716,283967,377918,495219,640000,816821,1030722,1287273,
%U A212242 1592524,1953125,2376276,2869777,3442078,4102229,4860000,5725831
%N A212242 Number of (u,v,w,x,y,z) with all terms in {0,1,...,n} and 5u=v+w+x+y+z.
%C A212242 u=average{v,w,x,y,z}.  For a guide to related sequences, see A211795.
%H A212242 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,2,-5,10,-10,5,-1).
%F A212242 a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5)-5a(n-6)+10a(n-7)-10a(n-8)+5a(n-9)-a(n-10).
%F A212242 G.f.: ( 1-3*x+53*x^2-51*x^3+120*x^4-51*x^5+53*x^6-3*x^7+x^8 ) / ( (x^4+x^3+x^2+x+1)*(x-1)^6 ). - _R. J. Mathar_, Jun 26 2012
%t A212242 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212242 (Do[If[5 u == v + w + x + y + z, s = s + 1], {u, 0, #}, {v, 0, #},{w, 0, #}, {x, 0, #}, {y, 0, #}, {z, 0, #}] &[n]; s)]];
%t A212242 Map[t[#] &, Range[0, 40]]   (* A212242 *)
%t A212242 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A212242 LinearRecurrence[{5,-10,10,-5,2,-5,10,-10,5,-1},{1,2,53,204,625,1556,3357,6558,11809,20000},40] (* _Harvey P. Dale_, Aug 20 2021 *)
%Y A212242 Cf. A211795, A212257, A212069.
%K A212242 nonn
%O A212242 0,2
%A A212242 _Clark Kimberling_, May 16 2012