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A200082
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T(n,k)=Number of 0..k arrays x(0..n) of n+1 elements with zero n-1st differences
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11
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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