|
%I #11 Dec 04 2017 09:05:20
%S 0,1,11,57,160,344,633,1051,1622,2370,3319,4493,5916,7612,9605,11919,
%T 14578,17606,21027,24865,29144,33888,39121,44867,51150,57994,65423,
%U 73461,82132,91460,101469,112183,123626,135822,148795,162569,177168,192616,208937
%N Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>2.
%C For a guide to related sequences, see A211422.
%H Colin Barker, <a href="/A211614/b211614.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F From _Colin Barker_, Dec 04 2017: (Start)
%F G.f.: x*(1 + 7*x + 19*x^2 - 6*x^3 + 3*x^4) / (1 - x)^4.
%F a(n) = (8*n^3 - 15*n^2 + 15*n - 12)/2 for n>1.
%F (End)
%t t = Compile[{{u, _Integer}},
%t Module[{s = 0}, (Do[If[w + x + y > 2, s = s + 1], {w, #}, {x, #}, {y, #}] &[ Flatten[{Reverse[-#], #} &[Range[1, u]]]]; s)]];
%t Map[t[#] &, Range[0, 60]] (* A211614 *)
%t FindLinearRecurrence[%]
%t (* _Peter J. C. Moses_, Apr 13 2012 *)
%t Join[{0, 1},LinearRecurrence[{4, -6, 4, -1},{11, 57, 160, 344},34]] (* _Ray Chandler_, Aug 02 2015 *)
%o (PARI) concat(0, Vec(x*(1 + 7*x + 19*x^2 - 6*x^3 + 3*x^4) / (1 - x)^4 + O(x^40))) \\ _Colin Barker_, Dec 04 2017
%Y Cf. A211422.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Apr 16 2012
|
