cp's OEIS Frontend

A212573 Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|>|x-y|+|y-z|.

%I A212573 #21 Jan 05 2025 05:53:41
%S A212573 0,0,2,10,36,92,202,386,680,1112,1730,2570,3692,5140,6986,9282,12112,
%T A212573 15536,19650,24522,30260,36940,44682,53570,63736,75272,88322,102986,
%U A212573 119420,137732,158090,180610,205472,232800,262786,295562,331332
%N A212573 Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|>|x-y|+|y-z|.
%C A212573 For a guide to related sequences, see A211795.
%H A212573 Bo Gyu Jeong, <a href="/A212573/b212573.txt">Table of n, a(n) for n = 0..1000</a>
%H A212573 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F A212573 a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).
%F A212573 From _Bruno Berselli_, Jun 14 2012: (Start)
%F A212573 G.f.: 2*(1-3*x+x^2+6*x^3-3*x^4+3*x^5+5*x^6)/((1+x)^2*(1-x)^5).
%F A212573 a(n) = (2*(n-3)*n*(5*n^2-15*n+31)-3*(2*n-3)*(-1)^n+87)/48. (End)
%t A212573 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212573 (Do[If[Abs[w - x] > Abs[x - y] + Abs[y - z], s = s + 1],
%t A212573 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212573 Map[t[#] &, Range[0, 40]]   (* A212573 *)
%t A212573 %/2  (* integers *)
%Y A212573 Cf. A211795, A212570.
%K A212573 nonn,easy
%O A212573 0,3
%A A212573 _Clark Kimberling_, May 22 2012