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

1,1

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

Links

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

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

Example

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

Crossrefs

Row 4 of A200763.

Sequence in context: A100104 A015650 A383539 * A285987 A055365 A209817

Adjacent sequences: A200761 A200762 A200763 * A200765 A200766 A200767

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved