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A212897 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)>1.

%I A212897 #14 Jun 17 2017 03:06:26
%S A212897 0,0,2,16,74,230,562,1172,2186,3754,6050,9272,13642,19406,26834,36220,
%T A212897 47882,62162,79426,100064,124490,153142,186482,224996,269194,319610,
%U A212897 376802,441352,513866,594974,685330,785612,896522,1018786
%N A212897 Number of (w,x,y,z) with all terms in {0,...,n} and (least gapsize)>1.
%C A212897 The gapsizes are |w-x|, |x-y|, |y-z|. Every term is even.
%C A212897 For a guide to related sequences, see A211795.
%H A212897 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A212897 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>=7.
%F A212897 G.f.: (2*x^2 + 6*x^3 + 14*x^4 + 2*x^6)/(1 - 5*x + 10*x^2 - 10*x^3 + 5*x^4 - x^5).
%F A212897 a(n) = n^4-5*n^3+12*n^2-16*n+10 with n>1, a(0)=a(1)=0. [_Bruno Berselli_, Jun 12 2012]
%t A212897 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212897 (Do[If[Min[Abs[w - x], Abs[x - y], Abs[y - z]] > 1, s = s + 1],
%t A212897 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212897 m = Map[t[#] &, Range[0, 40]]   (* A212897 *)
%t A212897 m/2 (* integers *)
%Y A212897 Cf. A211795.
%K A212897 nonn,easy
%O A212897 0,3
%A A212897 _Clark Kimberling_, May 31 2012