%I #13 Feb 20 2024 03:35:38

%S 1,1,3,5,7,10,14,17,22,27,32,38,45,51,59,67,75,84,94,103,114,125,136,

%T 148,161,173,187,201,215,230,246,261,278,295,312,330,349,367,387,407,

%U 427,448,470,491,514,537,560,584,609,633,659,685,711,738,766

%N Number of (w,x,y) with all terms in {0,...,n} and 2w = 3x+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 (1,1,0,-1,-1,1).

%F a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6).

%F G.f.: f(x)/g(x), where f(x) = 1 + x^2 + x^3 and g(x) = (1 + 2*x + 2*x^2 + x^3)*((1-x)^3).

%t t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[2 w == 3 x + y, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

%t m = Map[t[#] &, Range[0, 70]] (* A212986 *)

%Y Cf. A212959.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 04 2012