cp's OEIS Frontend

A212902 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<|x-y|<|y-z|.

%I A212902 #11 Jan 05 2025 05:53:27
%S A212902 0,0,2,14,44,110,228,426,726,1168,1780,2612,3700,5104,6866,9058,11728,
%T A212902 14958,18804,23358,28682,34880,42020,50216,59544,70128,82050,95446,
%U A212902 110404,127070,145540,165970,188462,213184,240244,269820,302028
%N A212902 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<|x-y|<|y-z|.
%C A212902 Every term is even.
%C A212902 For a guide to related sequences, see A211795.
%H A212902 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-3,-1,1,3,-1,-2,1).
%F A212902 a(n) = 2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)-a(n-7)-2*a(n-8)+a(n-9).
%F A212902 G.f.: (2*x^2 + 10*x^3 + 14*x^4 + 14*x^5 + 8*x^6 + 4*x^7 )/(1 - 2*x - x^2 + 3*x^3 + x^4 - x^5 - 3*x^6 + x^7 + 2*x^8 - x^9).
%t A212902 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212902 (Do[If[Abs[w - x] < Abs[x - y] < Abs[y - z], s = s + 1],
%t A212902 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212902 m = Map[t[#] &, Range[0, 40]]   (* A212902 *)
%t A212902 m/2 (* integers *)
%t A212902 LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {0, 0, 2, 14, 44, 110, 228, 426, 726}, 40]
%Y A212902 Cf. A211795.
%K A212902 nonn,easy
%O A212902 0,3
%A A212902 _Clark Kimberling_, Jun 01 2012