|
%I #17 Jun 13 2015 00:54:15
%S 0,4,16,44,92,168,276,424,616,860,1160,1524,1956,2464,3052,3728,4496,
%T 5364,6336,7420,8620,9944,11396,12984,14712,16588,18616,20804,23156,
%U 25680,28380,31264,34336,37604,41072,44748,48636,52744,57076
%N Number of (w,x,y) with all terms in {0,...,n} and |w-x| != |x-y|.
%C a(n)+A212959(n)=(n+1)^3. Every term is divisible by 4.
%C For a guide to related sequences, see A212959.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F G.f.: f(x)/g(x), where f(x)=4x(1+x^2+x^3) and g(x)=(1+x)(1-x)^4.
%F a(n) = (4*n^3 + 6*n^2 + 4*n+1 - (-1)^n)/4. - _Luce ETIENNE_, Apr 05 2014
%t t = Compile[{{n, _Integer}}, Module[{s = 0},
%t (Do[If[Abs[w - x] != Abs[x - y], s = s + 1],
%t {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
%t m = Map[t[#] &, Range[0, 45]] (* A212960 *)
%t m/4 (* integers *)
%Y Cf. A212959.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jun 01 2012
|
