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<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
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)]];
(Do[If[2 w == 3 x + y, s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
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<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
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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).
and g(x) = (1 + 2*x + 2*x^2 + x^3)((1-x)^3).
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Number of (w,x,y) with all terms in {0,...,n} and 2w = 3x+y.
a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6).
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).