cp's OEIS Frontend

A212574 Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|>=|x-y|+|y-z|.

%I A212574 #11 Jun 13 2015 00:54:14
%S A212574 0,1,8,33,88,197,380,673,1104,1721,2560,3681,5128,6973,9268,12097,
%T A212574 15520,19633,24504,30241,36920,44661,53548,63713,75248,88297,102960,
%U A212574 119393,137704,158061,180580,205441,232768,262753,295528,331297
%N A212574 Number of (w,x,y,z) with all terms in {1,...,n} and  |w-x|>=|x-y|+|y-z|.
%C A212574 For a guide to related sequences, see A211795.
%H A212574 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F A212574 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 A212574 G.f.: -x*(1+5*x+10*x^2+2*x^3+x^4+x^5) / ( (1+x)^2*(x-1)^5 ).
%t A212574 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212574 (Do[If[Abs[w - x] >= Abs[x - y] + Abs[y - z], s = s + 1],
%t A212574 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212574 Map[t[#] &, Range[0, 40]]   (* A212574 *)
%t A212574 LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {0, 1, 8, 33, 88, 197, 380}, 40]
%Y A212574 Cf. A211795, A212570.
%K A212574 nonn,easy
%O A212574 0,3
%A A212574 _Clark Kimberling_, May 22 2012