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%I #19 Mar 21 2017 10:57:46
%S 0,0,0,0,0,0,0,0,1,1,1,2,2,3,4,4,5,6,7,8,9,10,11,13,14,15,17,18,20,22,
%T 23,25,27,29,31,33,35,37,40,42,44,47,49,52,55,57,60,63,66,69,72,75,78,
%U 82,85,88,92,95,99,103,106,110,114,118,122,126,130,134,139
%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w=3x+5y.
%C For a guide to related sequences, see A211422.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, -1, 1, -1, 0, -1, 1).
%F a(n) = a(n-1)+a(n-3)-a(n-4)+a(n-5)-a(n-6)-a(n-8)+a(n-9).
%F G.f.: x^8/((1-x)*(1-x^3)*(1-x^5)).
%t t[n_] := t[n] = Flatten[Table[-w + 3 x + 5 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
%t c[n_] := Count[t[n], 0]
%t t = Table[c[n], {n, 0, 70}] (* A211524 *)
%t FindLinearRecurrence[t]
%t LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{0,0,0,0,0,0,0,0,1},69] (* _Ray Chandler_, Aug 02 2015 *)
%Y Cf. A008672, A211422.
%K nonn
%O 0,12
%A _Clark Kimberling_, Apr 14 2012
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