A213480 - OEIS

%I #18 Oct 27 2024 04:15:51

%S 0,4,16,46,95,175,285,439,634,886,1190,1564,2001,2521,3115,3805,4580,

%T 5464,6444,7546,8755,10099,11561,13171,14910,16810,18850,21064,23429,

%U 25981,28695,31609,34696,37996,41480,45190,49095,53239,57589

%N Number of (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) + A213479(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.: (4*x + 8*x^2 + 10*x^3 + 3*x^4 - x^5)/((1 - x)^4*(1 + x)^2).

%F a(n) = (8*n^3 + 15*n^2 + 4*n + 5 - (2*n+5)*((n+1) mod 2))/8. - _Ayoub Saber Rguez_, Nov 20 2021

%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]]   (* A213480 *)

%Y Cf. A212959.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jun 13 2012