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A212749 Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x<R, y<R, z<R, where R = max{w,x,y,z} - min{w,x,y,z}. 2

%I

%S 1,14,70,222,537,1116,2056,3512,5605,8550,12486,17694,24325,32732,

%T 43072,55776,71001,89262,110710,135950,165121,198924,237480,281592,

%U 331357,387686,450646,521262,599565,686700,782656,888704,1004785

%N Number of (w,x,y,z) with all terms in {0,...,n} and at least one of these conditions holds: w=R, x<R, y<R, z<R, where R = max{w,x,y,z} - min{w,x,y,z}.

%C For a guide to related sequences, see A211795.

%H <a href="/index/Rec#order_08">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.: ( -1-12*x-40*x^2-60*x^3-37*x^4-12*x^5 ) / ( (1+x)^3*(x-1)^5 ).

%t t = Compile[{{n, _Integer}},

%t Module[{s = 0}, (Do[

%t If[(w == # || x < # || y < # || z < #) &[

%t Max[w, x, y, z] - Min[w, x, y, z]], s++], {w, 0, n},

%t {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];

%t Map[t[#] &, Range[0, 40]] (* A212749 *)

%t (* _Peter J. C. Moses_, May 24 2012 *)

%Y Cf. A211795.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, May 27 2012

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Last modified May 8 09:21 EDT 2021. Contains 343666 sequences. (Running on oeis4.)