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A200764 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value.

%I A200764 #16 May 30 2025 23:54:09
%S A200764 5,19,51,113,219,388,638,995,1483,2133,2975,4047,5383,7028,9022,11415,
%T A200764 14253,17593,21485,25993,31173,37094,43818,51421,59969,69545,80221,
%U A200764 92085,105215,119706,135640,153119,172231,193083,215769,240403,267083,295930
%N A200764 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value.
%C A200764 a(n) is the number of integer lattice points in n*C where C is the polytope in R^4 with vertices [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1/3], [0, 1, 1, 1], [0, 1, 1, 2/3], [0, 1, 1/2, 1], [0, 1, 1/2, 1/2], [1, 1, 1, 1], and thus is an Ehrhart quasi-polynomial. - _Robert Israel_, May 30 2025
%H A200764 R. H. Hardin, <a href="/A200764/b200764.txt">Table of n, a(n) for n = 1..210</a>
%F A200764 Empirical: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) -a(n-4) +a(n-5) +3*a(n-6) -a(n-7) -2*a(n-8) +a(n-9).
%F A200764 Empirical g.f.: -x*(5+9*x+8*x^2+7*x^3+4*x^4+4*x^5-x^6-2*x^7+x^8) / ( (1+x+x^2)*(1+x)^2*(x-1)^5 ). - _R. J. Mathar_, Nov 22 2011
%e A200764 Some solutions for n=8
%e A200764 ..0....5....0....2....0....1....2....2....3....3....0....0....2....0....2....1
%e A200764 ..4....6....1....4....0....4....3....5....4....3....5....2....4....1....7....1
%e A200764 ..3....8....1....3....5....7....4....8....4....7....4....7....4....5....7....6
%e A200764 ..3....7....1....5....7....4....7....7....7....6....4....7....4....5....6....3
%Y A200764 Row 4 of A200763.
%K A200764 nonn
%O A200764 1,1
%A A200764 _R. H. Hardin_, Nov 22 2011