%I #12 Dec 03 2017 10:12:15
%S 0,0,0,0,1,1,1,2,3,4,5,6,7,9,11,12,14,16,18,21,23,25,28,31,34,37,40,
%T 43,47,51,54,58,62,66,71,75,79,84,89,94,99,104,109,115,121,126,132,
%U 138,144,151,157,163,170,177,184,191,198,205,213,221,228,236,244
%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x+5y.
%C For a guide to related sequences, see A211422.
%H Colin Barker, <a href="/A211543/b211543.txt">Table of n, a(n) for n = 0..1000</a>
%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^4*(1 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Dec 03 2017
%t t[n_] := t[n] = Flatten[Table[-2 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}] (* A211543 *)
%t FindLinearRecurrence[t]
%t LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{0,0,0,0,1,1,1,2,3},63] (* _Ray Chandler_, Aug 02 2015 *)
%o (PARI) concat(vector(4), Vec(x^4*(1 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ _Colin Barker_, Dec 03 2017
%Y Cf. A211422.
%K nonn,easy
%O 0,8
%A _Clark Kimberling_, Apr 15 2012