A200082 T(n,k)=Number of 0..k arrays x(0..n) of n+1 elements with zero n-1st differences.

1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 6, 3, 2, 1, 6, 9, 8, 7, 2, 1, 7, 12, 17, 14, 9, 2, 1, 8, 17, 26, 27, 18, 9, 2, 1, 9, 22, 43, 58, 37, 24, 15, 2, 1, 10, 27, 64, 111, 108, 85, 56, 7, 2, 1, 11, 34, 89, 182, 245, 202, 169, 26, 3, 2, 1, 12, 41, 122, 279, 454, 429, 394, 151, 26, 11, 2, 1, 13, 48

Offset: 1

Author

R. H. Hardin Nov 13 2011

Keywords

• nonn
• tabl

Comments

Table starts

.1..1..1...1...1....1.....1.....1.....1......1......1......1.......1.......1

.2..3..4...5...6....7.....8.....9....10.....11.....12.....13......14......15

.2..3..6...9..12...17....22....27....34.....41.....48.....57......66......75

.2..3..8..17..26...43....64....89...122....163....208....269.....334.....407

.2..7.14..27..58..111...182...279...404....617....872...1199....1580....2045

.2..9.18..37.108..245...454...759..1172...2001...3144...4663....6568....8945

.2..9.24..85.202..429..1046..2145..4022...6955..11438..17927...26868...41817

.2.15.56.169.394..855..2546..6179.12710..23899..41522..68427..106948..183797

.2..7.26.151.468.1863..5056.12965.29904..64603.124728.243309..432190..748301

.2..3.26.219.848.3573.11638.31507.84560.198435.418330.878657.1704398.3107463

T(n,k) is the number of integer lattice points in k*C(n) where C(n) is the polytope in R^(n+1) defined by two linear equations and the bounds 0 <= x_i <= 1. Since the vertices of this polytope have rational coordinates, T(n,k) for each fixed n is an Ehrhart quasi-polynomial of degree n-1. - Robert Israel, Nov 11 2019

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..268

Crossrefs

Row 3 is A008810(n+1)