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

5, 19, 51, 113, 219, 388, 638, 995, 1483, 2133, 2975, 4047, 5383, 7028, 9022, 11415, 14253, 17593, 21485, 25993, 31173, 37094, 43818, 51421, 59969, 69545, 80221, 92085, 105215, 119706, 135640, 153119, 172231, 193083, 215769, 240403, 267083, 295930

Offset: 1

Author

R. H. Hardin, Nov 22 2011

Keywords

• nonn

Comments

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

Examples

			Some solutions for n=8
..0....5....0....2....0....1....2....2....3....3....0....0....2....0....2....1
..4....6....1....4....0....4....3....5....4....3....5....2....4....1....7....1
..3....8....1....3....5....7....4....8....4....7....4....7....4....5....7....6
..3....7....1....5....7....4....7....7....7....6....4....7....4....5....6....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Row 4 of A200763.

Formula

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).

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