cp's OEIS Frontend

A212068 Number of (w,x,y,z) with all terms in {1,...,n} and 2w=x+y+z.

%I A212068 #15 Dec 02 2017 06:12:30
%S A212068 0,0,3,10,25,49,86,137,206,294,405,540,703,895,1120,1379,1676,2012,
%T A212068 2391,2814,3285,3805,4378,5005,5690,6434,7241,8112,9051,10059,11140,
%U A212068 12295,13528,14840,16235,17714,19281,20937,22686,24529,26470,28510,30653,32900
%N A212068 Number of (w,x,y,z) with all terms in {1,...,n} and 2w=x+y+z.
%C A212068 For a guide to related sequences, see A211795.
%H A212068 Colin Barker, <a href="/A212068/b212068.txt">Table of n, a(n) for n = 0..1000</a>
%H A212068 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A212068 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
%F A212068 From _Colin Barker_, Dec 02 2017: (Start)
%F A212068 G.f.: x^2*(3 + x + x^2) / ((1 - x)^4*(1 + x)).
%F A212068 a(n) = n*(10*n^2 - 3*n + 2)/24 for n even.
%F A212068 a(n) = (n - 1)*(10*n^2 + 7*n + 9)/24 for n odd.
%F A212068 (End)
%t A212068 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212068 (Do[If[2 w == x + y + z, s = s + 1],
%t A212068 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212068 Map[t[#] &, Range[0, 50]] (* A212068 *)
%t A212068 FindLinearRecurrence[%]
%t A212068 (* _Peter J. C. Moses_, Apr 13 2012 *)
%t A212068 LinearRecurrence[{3, -2, -2, 3, -1},{0, 0, 3, 10, 25},42] (* _Ray Chandler_, Aug 02 2015 *)
%o A212068 (PARI) concat(vector(2), Vec(x^2*(3 + x + x^2) / ((1 - x)^4*(1 + x)) + O(x^40))) \\ _Colin Barker_, Dec 02 2017
%Y A212068 Cf. A211795.
%K A212068 nonn,easy
%O A212068 0,3
%A A212068 _Clark Kimberling_, May 01 2012