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A212903 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<=|x-y|<=|y-z|.

%I A212903 #11 Jan 05 2025 05:53:24
%S A212903 1,8,35,94,209,398,697,1130,1743,2568,3661,5060,6833,9024,11711,14946,
%T A212903 18817,23382,28741,34958,42143,50368,59753,70376,82369,95816,110859,
%U A212903 127590,146161,166670,189281,214098,241295,270984,303349,338508
%N A212903 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|<=|x-y|<=|y-z|.
%C A212903 For a guide to related sequences, see A211795.
%H A212903 <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 A212903 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 A212903 G.f.: (1 + 6*x + 18*x^2 + 19*x^3 + 11*x^4 - 2*x^5 - 2*x^6 + 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 A212903 t = Compile[{{n, _Integer}}, Module[{s = 0},(Do[If[Abs[w - x] <= Abs[x - y] <= Abs[y - z], s = s + 1],
%t A212903 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212903 m = Map[t[#] &, Range[0, 40]]   (* A212903 *)
%t A212903 LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {1, 8, 35, 94, 209, 398, 697, 1130, 1743}, 40]
%Y A212903 Cf. A211795.
%K A212903 nonn,easy
%O A212903 0,2
%A A212903 _Clark Kimberling_, Jun 01 2012