cp's OEIS Frontend

A212755 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|=max{w,x,y,z}-min{w,x,y,z}.

%I A212755 #15 Aug 28 2025 15:39:58
%S A212755 1,10,37,96,205,386,665,1072,1641,2410,3421,4720,6357,8386,10865,
%T A212755 13856,17425,21642,26581,32320,38941,46530,55177,64976,76025,88426,
%U A212755 102285,117712,134821,153730,174561,197440,222497,249866,279685
%N A212755 Number of (w,x,y,z) with all terms in {0,...,n}  and |w-x|=max{w,x,y,z}-min{w,x,y,z}.
%C A212755 For a guide to related sequences, see A211795.
%H A212755 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A212755 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
%F A212755 G.f.: (-1-5*x+3*x^2-x^3)/(x-1)^5.
%F A212755 E.g.f.: exp(x)*(6 + 54*x + 54*x^2 + 14*x^3 + x^4)/6. - _Stefano Spezia_, Aug 28 2025
%t A212755 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212755 (Do[If[Abs[w - x] == Max[w, x, y, z] - Min[w, x, y, z], s = s + 1],
%t A212755 {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
%t A212755 Map[t[#] &, Range[0, 40]]   (* A212755 *)
%Y A212755 Cf. A211795.
%K A212755 nonn,easy,changed
%O A212755 0,2
%A A212755 _Clark Kimberling_, May 28 2012