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

1,3

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

Links

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

Example

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

Crossrefs

Row 3 is A008810(n+1)

Sequence in context: A167286 A249821 A249822 * A052310 A052313 A271355

Adjacent sequences: A200079 A200080 A200081 * A200083 A200084 A200085

Keyword

nonn,tabl

Author

R. H. Hardin Nov 13 2011

Status

approved