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A212978 Number of (w,x,y) with all terms in {0,...,n} and range = 2*n-w-x.

%I A212978 #22 Mar 16 2023 08:50:15
%S A212978 1,5,11,20,32,46,63,83,105,130,158,188,221,257,295,336,380,426,475,
%T A212978 527,581,638,698,760,825,893,963,1036,1112,1190,1271,1355,1441,1530,
%U A212978 1622,1716,1813,1913,2015,2120,2228,2338,2451,2567,2685,2806,2930
%N A212978 Number of (w,x,y) with all terms in {0,...,n} and range = 2*n-w-x.
%C A212978 For a guide to related sequences, see A212959.
%H A212978 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A212978 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).
%F A212978 G.f.: (1 + 3*x + 2*x^2 + 2*x^3)/((1 - x)^3*(1 + x + x^2)). [corrected by _Bruno Berselli_, Jan 23 2017]
%t A212978 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212978 (Do[If[Max[w, x, y] - Min[w, x, y] == 2 n - w - x,
%t A212978   s = s + 1],
%t A212978 {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t A212978 m = Map[t[#] &, Range[0, 60]]   (* A212978 *)
%t A212978 LinearRecurrence[{2,-1,1,-2,1},{1,5,11,20,32},50] (* _Harvey P. Dale_, Sep 30 2017 *)
%Y A212978 Cf. A212959.
%Y A212978 Second bisection of A281333.
%K A212978 nonn,easy
%O A212978 0,2
%A A212978 _Clark Kimberling_, Jun 03 2012