%I #19 Apr 02 2020 11:43:31

%S 0,0,1,1,3,3,6,7,11,11,17,18,24,25,33,34,43,44,54,56,67,68,81,83,96,

%T 98,113,115,131,133,150,153,171,173,193,196,216,219,241,244,267,270,

%U 294,298,323,326,353,357,384,388,417,421,451,455,486,491,523,527

%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x-4y.

%C For a guide to related sequences, see A211422.

%H Bo Gyu Jeong, <a href="/A211541/b211541.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,-1,-1,-1,0,1).

%F a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6)-a(n-7)+a(n-9).

%F G.f.: x^2*(1+x+2*x^2+x^3+x^4+x^5+x^6)/((1+x^2)*(1+x+x^2)*(1+x)^2*(1-x)^3). [_Bruno Berselli_, Jun 15 2012]

%t t[n_] := t[n] = Flatten[Table[2 w - 3 x + 4 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]

%t c[n_] := Count[t[n], 0]

%t t = Table[c[n], {n, 0, 80}] (* A211541 *)

%t FindLinearRecurrence[t]

%Y Cf. A211422.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 15 2012