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A212677 Number of (w,x,y,z) with all terms in {1,...,n} and w+y=|x-y|+|y-z|.

%I A212677 #7 Aug 01 2015 10:24:34
%S A212677 0,0,1,7,21,46,86,144,223,327,459,622,820,1056,1333,1655,2025,2446,
%T A212677 2922,3456,4051,4711,5439,6238,7112,8064,9097,10215,11421,12718,14110,
%U A212677 15600,17191,18887,20691,22606,24636,26784,29053,31447,33969
%N A212677 Number of (w,x,y,z) with all terms in {1,...,n} and w+y=|x-y|+|y-z|.
%C A212677 For a guide to related sequences, see A211795.
%H A212677 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 2, -3, 3, -1).
%F A212677 a(n)=3*a(n-1)-3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6).
%F A212677 G.f.: (x^2 + 4*x^3 + 3*x^4 + 2*x^5)/(1 - 3*x + 3* x^2 - 2*x^3 + 3*x^4 - 3*x^5 + x^6)
%t A212677 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212677 (Do[If[w + y == Abs[x - y] + Abs[y - z], s = s + 1],
%t A212677 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212677 Map[t[#] &, Range[0, 40]]   (* A212677 *)
%t A212677 LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 0, 1, 7, 21, 46}, 40]
%Y A212677 Cf. A211795.
%K A212677 nonn,easy
%O A212677 0,4
%A A212677 _Clark Kimberling_, May 23 2012