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A212246 Number of (w,x,y,z) with all terms in {1,...,n} and w <= x > y <= z.

%I A212246 #13 Jun 17 2017 03:06:25
%S A212246 0,0,4,21,65,155,315,574,966,1530,2310,3355,4719,6461,8645,11340,
%T A212246 14620,18564,23256,28785,35245,42735,51359,61226,72450,85150,99450,
%U A212246 115479,133371,153265,175305,199640,226424,255816,287980,323085
%N A212246 Number of (w,x,y,z) with all terms in {1,...,n} and w <= x > y <= z.
%C A212246 For a guide to related sequences, see A211795.
%H A212246 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A212246 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
%F A212246 G.f.: x^2*(4+x)/(1-x)^5. - _Bruno Berselli_, May 31 2012
%F A212246 a(n) = (n-1)*n*(n+1)*(5*n+6)/24. - _Bruno Berselli_, May 31 2012
%t A212246 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212246 (Do[If[w <= x > y <= z, s = s + 1],
%t A212246 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212246 Map[t[#] &, Range[0, 40]]   (* A212246 *)
%o A212246 (PARI) a(n) = n*(n-1)*(n+1)*(5*n+6)/24 \\ _Charles R Greathouse IV_, Feb 16 2015
%Y A212246 Cf. A211795.
%K A212246 nonn,easy
%O A212246 0,3
%A A212246 _Clark Kimberling_, May 19 2012
%E A212246 Offset corrected by _Charles R Greathouse IV_, Feb 16 2015