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A212676 Number of (w,x,y,z) with all terms in {1,...,n} and w+x=|x-y|+|y-z|.

%I A212676 #8 Aug 01 2015 10:24:13
%S A212676 0,0,1,9,23,52,92,155,234,344,475,645,841,1084,1358,1687,2052,2480,
%T A212676 2949,3489,4075,4740,5456,6259,7118,8072,9087,10205,11389,12684,14050,
%U A212676 15535,17096,18784,20553,22457,24447,26580,28804,31179,33650
%N A212676 Number of (w,x,y,z) with all terms in {1,...,n} and w+x=|x-y|+|y-z|.
%C A212676 For a guide to related sequences, see A211795.
%H A212676 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).
%F A212676 a(n)=2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
%F A212676 G.f.: (x^2 + 7*x^3 + 4*x^4 + x^5)/(1 - 2 x - x^2 + 4 x^3 - x^4 - 2 x^5 + x^6)
%t A212676 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212676 (Do[If[w + x == Abs[x - y] + Abs[y - z], s = s + 1],
%t A212676 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212676 Map[t[#] &, Range[0, 40]]   (* A212676 *)
%t A212676 LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 0, 1, 9, 23, 52}, 41]
%Y A212676 Cf. A211795.
%K A212676 nonn,easy
%O A212676 0,4
%A A212676 _Clark Kimberling_, May 23 2012