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%I #21 Dec 31 2021 09:54:45
%S 1,7,25,59,117,202,323,482,689,945,1261,1637,2085,2604,3207,3892,4673,
%T 5547,6529,7615,8821,10142,11595,13174,14897,16757,18773,20937,23269,
%U 25760,28431,31272,34305,37519,40937,44547,48373,52402,56659
%N Number of triples (w,x,y) with all terms in {0,...,n} and |w-x| + |x-y| <= w+x+y.
%C For a guide to related sequences, see A212959.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F a(n) + A006918(n) = (n+1)^3.
%F a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F G.f.: (1 + 5*x + 10*x^2 + 6*x^3 + x^4)/((1 - x)^4 (1 + x)^2)).
%F From _Ayoub Saber Rguez_, Dec 29 2021: (Start)
%F a(n) = A213482(n) + A213479(n).
%F a(n) = (23*n^3 + 66*n^2 + 64*n + 24 - (3*n+6)*(n mod 2))/24. (End)
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[w + x + y >= Abs[w - x] + Abs[x - y], s = s + 1],
%t {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t Map[t[#] &, Range[0, 60]] (* A213481 *)
%Y Cf. A212959, A213479, A213482.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 13 2012
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