A211628 - OEIS

%I #12 Dec 05 2017 08:22:53

%S 0,4,30,105,249,487,846,1346,2012,2871,3943,5253,6828,8688,10858,

%T 13365,16229,19475,23130,27214,31752,36771,42291,48337,54936,62108,

%U 69878,78273,87313,97023,107430,118554,130420,143055,156479,170717,185796,201736,218562

%N Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and 3w+x+y>0.

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

%H Colin Barker, <a href="/A211628/b211628.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).

%F a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n>5.

%F G.f.: x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)). - _Colin Barker_, Dec 05 2017

%t t = Compile[{{u, _Integer}},

%t    Module[{s = 0}, (Do[If[3 w + x + y > 0,

%t          s = s + 1], {w, #}, {x, #}, {y, #}] &[

%t       Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];

%t Map[t[#] &, Range[0, 60]]   (* A211628 *)

%t FindLinearRecurrence[%]

%t (* _Peter J. C. Moses_, Apr 13 2012 *)

%t LinearRecurrence[{3, -3, 2, -3, 3, -1},{0, 4, 30, 105, 249, 487},36] (* _Ray Chandler_, Aug 02 2015 *)

%o (PARI) concat(0, Vec(x*(4 + 18*x + 27*x^2 + 16*x^3 + 7*x^4) / ((1 - x)^4*(1 + x + x^2)) + O(x^40))) \\ _Colin Barker_, Dec 05 2017

%Y Cf. A211422.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Apr 17 2012