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A200252 Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).

%I A200252 #16 Feb 19 2018 08:26:12
%S A200252 5,12,26,45,75,112,164,225,305,396,510,637,791,960,1160,1377,1629,
%T A200252 1900,2210,2541,2915,3312,3756,4225,4745,5292,5894,6525,7215,7936,
%U A200252 8720,9537,10421,11340,12330,13357,14459,15600,16820,18081,19425,20812,22286,23805
%N A200252 Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).
%C A200252 Row 3 of A200251.
%C A200252 a(n) = A199771(n+1). - _Reinhard Zumkeller_, Nov 23 2011
%H A200252 R. H. Hardin, <a href="/A200252/b200252.txt">Table of n, a(n) for n = 1..210</a>
%H A200252 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A200252 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A200252 From _Colin Barker_, Feb 19 2018: (Start)
%F A200252 G.f.: x*(5 + 2*x - 3*x^2 + x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
%F A200252 a(n) = (n^3 + 5*n^2 + 8*n + 4) / 4 for n even.
%F A200252 a(n) = (n^3 + 5*n^2 + 9*n + 5) / 4 for n odd.
%F A200252 (End)
%e A200252 Some solutions for n=6:
%e A200252   2  0  0  3  3  1  4  0  1  3  0  3  0  2  1  3
%e A200252   6  5  3  6  3  1  5  2  4  6  6  5  0  5  2  4
%e A200252   2  6  6  2  6  4  4  2  6  5  6  5  6  5  4  0
%K A200252 nonn,easy
%O A200252 1,1
%A A200252 _R. H. Hardin_, Nov 15 2011