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A212675 Number of (w,x,y,z) with all terms in {1,...,n} and w >= |x-y| + |y-z|.

%I A212675 #16 May 10 2019 18:28:08
%S A212675 0,1,14,57,158,353,688,1217,2004,3121,4650,6681,9314,12657,16828,
%T A212675 21953,28168,35617,44454,54841,66950,80961,97064,115457,136348,159953,
%U A212675 186498,216217,249354,286161,326900,371841,421264,475457,534718
%N A212675 Number of (w,x,y,z) with all terms in {1,...,n} and  w >= |x-y| + |y-z|.
%C A212675 a(n) + A212568(n) = n^4.
%C A212675 For a guide to related sequences, see A211795.
%H A212675 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 0, 5, -4, 1).
%F A212675 a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
%F A212675 G.f.: (x + 10*x^2 + 6*x^3 + x^5)/(1 - 4*x + 5*x^2 - 5*x^4 + 4*x^5 - x^6). [corrected by _Georg Fischer_, May 10 2019]
%t A212675 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212675 (Do[If[w >= Abs[x - y] + Abs[y - z], s = s + 1],
%t A212675 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212675 Map[t[#] &, Range[0, 40]]   (* A212675 *)
%t A212675 LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 14, 57, 158, 353}, 40]
%Y A212675 Cf. A211795.
%K A212675 nonn,easy
%O A212675 0,3
%A A212675 _Clark Kimberling_, May 23 2012