A212987 - OEIS

%I #12 Feb 20 2024 03:36:36

%S 1,1,3,5,8,10,16,18,25,29,37,41,52,56,68,74,87,93,109,115,132,140,158,

%T 166,187,195,217,227,250,260,286,296,323,335,363,375,406,418,450,464,

%U 497,511,547,561,598,614,652,668,709,725,767,785,828,846,892

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

%C For a guide to related sequences, see A212959.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1,-2,0,1).

%F a(n) = 2*a(n-2)+a(n-3)-a(n-4)-2*a(n-5)+a(n-7).

%F G.f.: f(x)/g(x), where f(x) = 1 + x + x^2 + 2*x^3 + 2*x^4 and g(x) = (1 + x + x^2)((1+x)^2)((1-x)^3).

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

%t m = Map[t[#] &, Range[0, 70]]   (* A212987 *)

%Y Cf. A212959.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 04 2012